Migrate 'Global styles sidebar' test to Playwright (#55045)

* Migrate 'Global styles sidebar' test to Playwright
* Remove old test file

test/e2e/specs/site-editor/global-styles-sidebar.spec.js

@@ -0,0 +1,49 @@
+/**
+ * WordPress dependencies
+ */
+const { test, expect } = require( '@wordpress/e2e-test-utils-playwright' );
+
+test.describe( 'Global styles sidebar', () => {
+	test.beforeAll( async ( { requestUtils } ) => {
+		await requestUtils.activateTheme( 'emptytheme' );
+	} );
+
+	test.afterAll( async ( { requestUtils } ) => {
+		await requestUtils.activateTheme( 'twentytwentyone' );
+	} );
+
+	test.beforeEach( async ( { admin, editor } ) => {
+		await admin.visitSiteEditor( {
+			postId: 'emptytheme//index',
+			postType: 'wp_template',
+		} );
+		await editor.canvas.click( 'body' );
+	} );
+
+	test( 'should filter blocks list results', async ( { page } ) => {
+		// Navigate to Styles -> Blocks.
+		await page
+			.getByRole( 'region', { name: 'Editor top bar' } )
+			.getByRole( 'button', { name: 'Styles' } )
+			.click();
+		await page
+			.getByRole( 'region', { name: 'Editor settings' } )
+			.getByRole( 'button', { name: 'Blocks styles' } )
+			.click();
+
+		await page
+			.getByRole( 'searchbox', { name: 'Search for blocks' } )
+			.fill( 'heading' );
+
+		// Matches both Heading and Table of Contents blocks.
+		// The latter contains "heading" in its description.
+		await expect(
+			page.getByRole( 'button', { name: 'Heading block styles' } )
+		).toBeVisible();
+		await expect(
+			page.getByRole( 'button', {
+				name: 'Table of Contents block styles',
+			} )
+		).toBeVisible();
+	} );
+} );