diff --git a/wp-includes/block-template-utils.php b/wp-includes/block-template-utils.php
index 54413d809b..a16fe2914c 100644
--- a/wp-includes/block-template-utils.php
+++ b/wp-includes/block-template-utils.php
@@ -147,7 +147,7 @@ function get_default_block_template_types() {
 		),
 		'category'       => array(
 			'title'       => _x( 'Category', 'Template name' ),
-			'description' => __( 'Displays latest posts in single post category.' ),
+			'description' => __( 'Displays latest posts from a single post category.' ),
 		),
 		'taxonomy'       => array(
 			'title'       => _x( 'Taxonomy', 'Template name' ),
@@ -555,7 +555,8 @@ function _build_block_template_result_from_post( $post ) {
 	$template_file  = _get_block_template_file( $post->post_type, $post->post_name );
 	$has_theme_file = wp_get_theme()->get_stylesheet() === $theme && null !== $template_file;
 
-	$origin = get_post_meta( $post->ID, 'origin', true );
+	$origin           = get_post_meta( $post->ID, 'origin', true );
+	$is_wp_suggestion = get_post_meta( $post->ID, 'is_wp_suggestion', true );
 
 	$template                 = new WP_Block_Template();
 	$template->wp_id          = $post->ID;
@@ -570,7 +571,7 @@ function _build_block_template_result_from_post( $post ) {
 	$template->title          = $post->post_title;
 	$template->status         = $post->post_status;
 	$template->has_theme_file = $has_theme_file;
-	$template->is_custom      = true;
+	$template->is_custom      = empty( $is_wp_suggestion );
 	$template->author         = $post->post_author;
 
 	if ( 'wp_template' === $post->post_type && $has_theme_file && isset( $template_file['postTypes'] ) ) {
@@ -679,7 +680,8 @@ function get_block_templates( $query = array(), $template_type = 'wp_template' )
 			continue;
 		}
 
-		if ( $post_type &&
+		if (
+			$post_type &&
 			isset( $template->post_types ) &&
 			! in_array( $post_type, $template->post_types, true )
 		) {
@@ -912,9 +914,10 @@ function block_footer_area() {
  * @return Bool Whether this file is in an ignored directory.
  */
 function wp_is_theme_directory_ignored( $path ) {
-	$directories_to_ignore = array( '.svn', '.git', '.hg', '.bzr', 'node_modules', 'vendor' );
+	$directories_to_ignore = array( '.DS_Store', '.svn', '.git', '.hg', '.bzr', 'node_modules', 'vendor' );
+
 	foreach ( $directories_to_ignore as $directory ) {
-		if ( strpos( $path, $directory ) === 0 ) {
+		if ( str_starts_with( $path, $directory ) ) {
 			return true;
 		}
 	}
@@ -1023,3 +1026,74 @@ function wp_generate_block_templates_export_file() {
 
 	return $filename;
 }
+
+/**
+ * Gets the template hierarchy for the given template slug to be created.
+ *
+ *
+ * Note: Always add `index` as the last fallback template.
+ *
+ * @since 6.1.0
+ *
+ * @param string  $slug           The template slug to be created.
+ * @param boolean $is_custom      Optional. Indicates if a template is custom or
+ *                                part of the template hierarchy. Default false.
+ * @param string $template_prefix Optional. The template prefix for the created template.
+ *                                Used to extract the main template type, e.g.
+ *                                in `taxonomy-books` the `taxonomy` is extracted.
+ *                                Default empty string.
+ * @return string[] The template hierarchy.
+ */
+function get_template_hierarchy( $slug, $is_custom = false, $template_prefix = '' ) {
+	if ( 'index' === $slug ) {
+		return array( 'index' );
+	}
+	if ( $is_custom ) {
+		return array( 'page', 'singular', 'index' );
+	}
+	if ( 'front-page' === $slug ) {
+		return array( 'front-page', 'home', 'index' );
+	}
+
+	$template_hierarchy = array( $slug );
+
+	// Most default templates don't have `$template_prefix` assigned.
+	if ( $template_prefix ) {
+		list( $type ) = explode( '-', $template_prefix );
+		// These checks are needed because the `$slug` above is always added.
+		if ( ! in_array( $template_prefix, array( $slug, $type ), true ) ) {
+			$template_hierarchy[] = $template_prefix;
+		}
+		if ( $slug !== $type ) {
+			$template_hierarchy[] = $type;
+		}
+	}
+
+	// Handle `archive` template.
+	if (
+		str_starts_with( $slug, 'author' ) ||
+		str_starts_with( $slug, 'taxonomy' ) ||
+		str_starts_with( $slug, 'category' ) ||
+		str_starts_with( $slug, 'tag' ) ||
+		'date' === $slug
+	) {
+		$template_hierarchy[] = 'archive';
+	}
+	// Handle `single` template.
+	if ( 'attachment' === $slug ) {
+		$template_hierarchy[] = 'single';
+	}
+
+	// Handle `singular` template.
+	if (
+		str_starts_with( $slug, 'single' ) ||
+		str_starts_with( $slug, 'page' ) ||
+		'attachment' === $slug
+	) {
+		$template_hierarchy[] = 'singular';
+	}
+
+	$template_hierarchy[] = 'index';
+
+	return $template_hierarchy;
+};
diff --git a/wp-includes/rest-api/endpoints/class-wp-rest-post-types-controller.php b/wp-includes/rest-api/endpoints/class-wp-rest-post-types-controller.php
index cb2daa4b29..8223f1dd6f 100644
--- a/wp-includes/rest-api/endpoints/class-wp-rest-post-types-controller.php
+++ b/wp-includes/rest-api/endpoints/class-wp-rest-post-types-controller.php
@@ -186,54 +186,58 @@ class WP_REST_Post_Types_Controller extends WP_REST_Controller {
 		$fields = $this->get_fields_for_response( $request );
 		$data   = array();
 
-		if ( in_array( 'capabilities', $fields, true ) ) {
+		if ( rest_is_field_included( 'capabilities', $fields ) ) {
 			$data['capabilities'] = $post_type->cap;
 		}
 
-		if ( in_array( 'description', $fields, true ) ) {
+		if ( rest_is_field_included( 'description', $fields ) ) {
 			$data['description'] = $post_type->description;
 		}
 
-		if ( in_array( 'hierarchical', $fields, true ) ) {
+		if ( rest_is_field_included( 'hierarchical', $fields ) ) {
 			$data['hierarchical'] = $post_type->hierarchical;
 		}
 
-		if ( in_array( 'visibility', $fields, true ) ) {
+		if ( rest_is_field_included( 'visibility', $fields ) ) {
 			$data['visibility'] = array(
 				'show_in_nav_menus' => (bool) $post_type->show_in_nav_menus,
 				'show_ui'           => (bool) $post_type->show_ui,
 			);
 		}
 
-		if ( in_array( 'viewable', $fields, true ) ) {
+		if ( rest_is_field_included( 'viewable', $fields ) ) {
 			$data['viewable'] = is_post_type_viewable( $post_type );
 		}
 
-		if ( in_array( 'labels', $fields, true ) ) {
+		if ( rest_is_field_included( 'labels', $fields ) ) {
 			$data['labels'] = $post_type->labels;
 		}
 
-		if ( in_array( 'name', $fields, true ) ) {
+		if ( rest_is_field_included( 'name', $fields ) ) {
 			$data['name'] = $post_type->label;
 		}
 
-		if ( in_array( 'slug', $fields, true ) ) {
+		if ( rest_is_field_included( 'slug', $fields ) ) {
 			$data['slug'] = $post_type->name;
 		}
 
-		if ( in_array( 'supports', $fields, true ) ) {
+		if ( rest_is_field_included( 'icon', $fields ) ) {
+			$data['icon'] = $post_type->menu_icon;
+		}
+
+		if ( rest_is_field_included( 'supports', $fields ) ) {
 			$data['supports'] = $supports;
 		}
 
-		if ( in_array( 'taxonomies', $fields, true ) ) {
+		if ( rest_is_field_included( 'taxonomies', $fields ) ) {
 			$data['taxonomies'] = array_values( $taxonomies );
 		}
 
-		if ( in_array( 'rest_base', $fields, true ) ) {
+		if ( rest_is_field_included( 'rest_base', $fields ) ) {
 			$data['rest_base'] = $base;
 		}
 
-		if ( in_array( 'rest_namespace', $fields, true ) ) {
+		if ( rest_is_field_included( 'rest_namespace', $fields ) ) {
 			$data['rest_namespace'] = $namespace;
 		}
 
@@ -287,6 +291,7 @@ class WP_REST_Post_Types_Controller extends WP_REST_Controller {
 	 * @since 4.7.0
 	 * @since 4.8.0 The `supports` property was added.
 	 * @since 5.9.0 The `visibility` and `rest_namespace` properties were added.
+	 * @since 6.1.0 The `icon` property was added.
 	 *
 	 * @return array Item schema data.
 	 */
@@ -385,6 +390,12 @@ class WP_REST_Post_Types_Controller extends WP_REST_Controller {
 						),
 					),
 				),
+				'icon'           => array(
+					'description' => __( 'The icon for the post type.' ),
+					'type'        => array( 'string', 'null' ),
+					'context'     => array( 'view', 'edit', 'embed' ),
+					'readonly'    => true,
+				),
 			),
 		);
 
diff --git a/wp-includes/rest-api/endpoints/class-wp-rest-templates-controller.php b/wp-includes/rest-api/endpoints/class-wp-rest-templates-controller.php
index 7e60674890..e26b4d17e5 100644
--- a/wp-includes/rest-api/endpoints/class-wp-rest-templates-controller.php
+++ b/wp-includes/rest-api/endpoints/class-wp-rest-templates-controller.php
@@ -42,6 +42,7 @@ class WP_REST_Templates_Controller extends WP_REST_Controller {
 	 * Registers the controllers routes.
 	 *
 	 * @since 5.8.0
+	 * @since 6.1.0 Endpoint for fallback template content.
 	 */
 	public function register_routes() {
 		// Lists all templates.
@@ -65,6 +66,34 @@ class WP_REST_Templates_Controller extends WP_REST_Controller {
 			)
 		);
 
+		// Get fallback template content.
+		register_rest_route(
+			$this->namespace,
+			'/' . $this->rest_base . '/lookup',
+			array(
+				array(
+					'methods'             => WP_REST_Server::READABLE,
+					'callback'            => array( $this, 'get_template_fallback' ),
+					'permission_callback' => array( $this, 'get_item_permissions_check' ),
+					'args'                => array(
+						'slug'            => array(
+							'description' => __( 'The slug of the template to get the fallback for' ),
+							'type'        => 'string',
+							'required'    => true,
+						),
+						'is_custom'       => array(
+							'description' => __( ' Indicates if a template is custom or part of the template hierarchy' ),
+							'type'        => 'boolean',
+						),
+						'template_prefix' => array(
+							'description' => __( 'The template prefix for the created template. This is used to extract the main template type, e.g. in `taxonomy-books` extracts the `taxonomy`' ),
+							'type'        => 'string',
+						),
+					),
+				),
+			)
+		);
+
 		// Lists/updates a single template based on the given id.
 		register_rest_route(
 			$this->namespace,
@@ -117,6 +146,21 @@ class WP_REST_Templates_Controller extends WP_REST_Controller {
 		);
 	}
 
+	/**
+	 * Returns the fallback template for the given slug.
+	 *
+	 * @since 6.1.0
+	 *
+	 * @param WP_REST_Request $request The request instance.
+	 * @return WP_REST_Response|WP_Error
+	 */
+	public function get_template_fallback( $request ) {
+		$hierarchy         = get_template_hierarchy( $request['slug'], $request['is_custom'], $request['template_prefix'] );
+		$fallback_template = resolve_block_template( $request['slug'], $hierarchy, '' );
+		$response          = $this->prepare_item_for_response( $fallback_template, $request );
+		return rest_ensure_response( $response );
+	}
+
 	/**
 	 * Checks if the user has permissions to make the request.
 	 *
@@ -525,6 +569,15 @@ class WP_REST_Templates_Controller extends WP_REST_Controller {
 			$changes->post_excerpt = $template->description;
 		}
 
+		if ( 'wp_template' === $this->post_type && isset( $request['is_wp_suggestion'] ) ) {
+			$changes->meta_input     = wp_parse_args(
+				array(
+					'is_wp_suggestion' => $request['is_wp_suggestion'],
+				),
+				$changes->meta_input = array()
+			);
+		}
+
 		if ( 'wp_template_part' === $this->post_type ) {
 			if ( isset( $request['area'] ) ) {
 				$changes->tax_input['wp_template_part_area'] = _filter_block_template_part_area( $request['area'] );
diff --git a/wp-includes/version.php b/wp-includes/version.php
index fefafaad78..b413168572 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -16,7 +16,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '6.1-alpha-54268';
+$wp_version = '6.1-alpha-54269';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.