Migrate 'container blocks' e2e tests to Playwright (#56141)

* Migrate 'Container block without paragraph support' tests
* Migrate 'InnerBlocks Template Sync' tests
* Remove old test files

test/e2e/specs/editor/plugins/container-blocks.spec.js

@@ -0,0 +1,50 @@
+/**
+ * WordPress dependencies
+ */
+const { test, expect } = require( '@wordpress/e2e-test-utils-playwright' );
+
+test.describe( 'Container block without paragraph support', () => {
+	test.beforeAll( async ( { requestUtils } ) => {
+		await requestUtils.activatePlugin(
+			'gutenberg-test-container-block-without-paragraph'
+		);
+	} );
+
+	test.beforeEach( async ( { admin } ) => {
+		await admin.createNewPost();
+	} );
+
+	test.afterAll( async ( { requestUtils } ) => {
+		await requestUtils.deactivatePlugin(
+			'gutenberg-test-container-block-without-paragraph'
+		);
+	} );
+
+	test( 'ensures we can use the alternative block appender properly', async ( {
+		editor,
+		page,
+	} ) => {
+		await editor.insertBlock( {
+			name: 'test/container-without-paragraph',
+		} );
+
+		await page
+			.getByRole( 'document', {
+				name: 'Block: Container without paragraph',
+			} )
+			.getByRole( 'button', { name: 'Add block' } )
+			.click();
+
+		await page
+			.getByRole( 'listbox', { name: 'Blocks' } )
+			.getByRole( 'option', { name: 'Image' } )
+			.click();
+
+		await expect.poll( editor.getBlocks ).toMatchObject( [
+			{
+				name: 'test/container-without-paragraph',
+				innerBlocks: [ { name: 'core/image' } ],
+			},
+		] );
+	} );
+} );