Rebase this PR on WordPress#2014 PR (because we've renamed the methods).

src/wp-admin/includes/theme.php

@@ -782,7 +782,7 @@ function wp_prepare_themes_for_js( $themes = null ) {
 					? wp_nonce_url( admin_url( 'themes.php?action=' . $auto_update_action . '&stylesheet=' . $encoded_slug ), 'updates' )
 					: null,
 			),
-			'block_based'    => $theme->is_block_based(),
+			'block_theme'    => $theme->is_block_theme(),
 		);
 	}
 

src/wp-includes/class-wp-customize-manager.php

@@ -5811,7 +5811,7 @@ public function handle_load_themes_request() {
 			$themes = array( 'themes' => array() );
 			foreach ( wp_prepare_themes_for_js() as $theme ) {
 				// Block-based themes should not be edited with Customizer.
-				if ( ! empty( $theme['block_based'] ) ) {
+				if ( ! empty( $theme['block_theme'] ) ) {
 					continue;
 				}
 				$theme['type']      = 'installed';

tests/phpunit/tests/ajax/CustomizeManager.php

@@ -743,7 +743,7 @@ public function test_wp_ajax_customize_load_themes_action() {
 			$this->assertNotEmpty( $theme['id'] );
 			$this->assertNotEmpty( $theme['name'] );
 			// It must only return non-block themes
-			$this->assertNotTrue( $theme['block_based'] );
+			$this->assertNotTrue( $theme['block_theme'] );
 		}
 	}
 }