diff --git a/src/wp-admin/site-editor.php b/src/wp-admin/site-editor.php
index cbbf38e7ea2c9..7706595172b6e 100644
--- a/src/wp-admin/site-editor.php
+++ b/src/wp-admin/site-editor.php
@@ -49,7 +49,7 @@ static function( $classes ) {
 	$indexed_template_types[] = $template_type;
 }
 
-$block_editor_context = new WP_Block_Editor_Context();
+$block_editor_context = new WP_Block_Editor_Context( array( 'name' => 'core/edit-site' ) );
 $custom_settings      = array(
 	'siteUrl'                              => site_url(),
 	'postsPerPage'                         => get_option( 'posts_per_page' ),
diff --git a/src/wp-admin/widgets-form-blocks.php b/src/wp-admin/widgets-form-blocks.php
index 563bbf2a699d9..ee3cb37734d3b 100644
--- a/src/wp-admin/widgets-form-blocks.php
+++ b/src/wp-admin/widgets-form-blocks.php
@@ -15,7 +15,7 @@
 $current_screen = get_current_screen();
 $current_screen->is_block_editor( true );
 
-$block_editor_context = new WP_Block_Editor_Context();
+$block_editor_context = new WP_Block_Editor_Context( array( 'name' => 'core/edit-widgets' ) );
 
 $preload_paths = array(
 	array( rest_get_route_for_post_type_items( 'attachment' ), 'OPTIONS' ),
diff --git a/src/wp-includes/class-wp-block-editor-context.php b/src/wp-includes/class-wp-block-editor-context.php
index 92957f3bd8b52..fd594bcad0e57 100644
--- a/src/wp-includes/class-wp-block-editor-context.php
+++ b/src/wp-includes/class-wp-block-editor-context.php
@@ -7,17 +7,29 @@
  */
 
 /**
- * Class representing a current block editor context.
- *
- * The expectation is that block editor can have a different set
- * of requirements on every screen where it is used. This class
- * allows to define supporting settings that can be used with filters.
+ * Contains information about a block editor being rendered.
  *
  * @since 5.8.0
  */
 final class WP_Block_Editor_Context {
 	/**
-	 * Post being edited. Optional.
+	 * String that identifies the block editor being rendered. Can be one of:
+	 *
+	 * - `'core/edit-post'`         - The post editor at `/wp-admin/edit.php`.
+	 * - `'core/edit-widgets'`      - The widgets editor at `/wp-admin/widgets.php`.
+	 * - `'core/customize-widgets'` - The widgets editor at `/wp-admin/customize.php`.
+	 * - `'core/edit-site'`         - The site editor at `/wp-admin/site-editor.php`.
+	 *
+	 * Defaults to 'core/edit-post'.
+	 *
+	 * @since 6.0.0
+	 *
+	 * @var string
+	 */
+	public $name = 'core/edit-post';
+
+	/**
+	 * The post being edited by the block editor. Optional.
 	 *
 	 * @since 5.8.0
 	 *
@@ -35,6 +47,9 @@ final class WP_Block_Editor_Context {
 	 * @param array $settings The list of optional settings to expose in a given context.
 	 */
 	public function __construct( array $settings = array() ) {
+		if ( isset( $settings['name'] ) ) {
+			$this->name = $settings['name'];
+		}
 		if ( isset( $settings['post'] ) ) {
 			$this->post = $settings['post'];
 		}
diff --git a/src/wp-includes/class-wp-customize-widgets.php b/src/wp-includes/class-wp-customize-widgets.php
index 8edcd6f1c9b43..1b6fe0a61021f 100644
--- a/src/wp-includes/class-wp-customize-widgets.php
+++ b/src/wp-includes/class-wp-customize-widgets.php
@@ -838,7 +838,11 @@ public function enqueue_scripts() {
 		 */
 
 		if ( wp_use_widgets_block_editor() ) {
-			$block_editor_context = new WP_Block_Editor_Context();
+			$block_editor_context = new WP_Block_Editor_Context(
+				array(
+					'name' => 'core/customize-widgets',
+				)
+			);
 
 			$editor_settings = get_block_editor_settings(
 				get_legacy_widget_block_editor_settings(),
diff --git a/tests/phpunit/tests/blocks/editor.php b/tests/phpunit/tests/blocks/editor.php
index a7277d596652d..9eadae9941443 100644
--- a/tests/phpunit/tests/blocks/editor.php
+++ b/tests/phpunit/tests/blocks/editor.php
@@ -80,6 +80,7 @@ public function filter_set_block_editor_settings_post( $editor_settings, $post )
 	public function test_block_editor_context_no_settings() {
 		$context = new WP_Block_Editor_Context();
 
+		$this->assertSame( 'core/edit-post', $context->name );
 		$this->assertNull( $context->post );
 	}
 
@@ -89,9 +90,40 @@ public function test_block_editor_context_no_settings() {
 	public function test_block_editor_context_post() {
 		$context = new WP_Block_Editor_Context( array( 'post' => get_post() ) );
 
+		$this->assertSame( 'core/edit-post', $context->name );
 		$this->assertSame( get_post(), $context->post );
 	}
 
+	/**
+	 * @ticket 55301
+	 */
+	public function test_block_editor_context_widgets() {
+		$context = new WP_Block_Editor_Context( array( 'name' => 'core/edit-widgets' ) );
+
+		$this->assertSame( 'core/edit-widgets', $context->name );
+		$this->assertNull( $context->post );
+	}
+
+	/**
+	 * @ticket 55301
+	 */
+	public function test_block_editor_context_widgets_customizer() {
+		$context = new WP_Block_Editor_Context( array( 'name' => 'core/customize-widgets' ) );
+
+		$this->assertSame( 'core/customize-widgets', $context->name );
+		$this->assertNull( $context->post );
+	}
+
+	/**
+	 * @ticket 55301
+	 */
+	public function test_block_editor_context_site() {
+		$context = new WP_Block_Editor_Context( array( 'name' => 'core/edit-site' ) );
+
+		$this->assertSame( 'core/edit-site', $context->name );
+		$this->assertNull( $context->post );
+	}
+
 	/**
 	 * @ticket 52920
 	 * @expectedDeprecated block_categories