Try: @swc/jest for transformation

client/__mocks__/file-transformer.js

@@ -0,0 +1,9 @@
+const path = require( 'path' );
+
+module.exports = {
+	process( sourceText, sourcePath ) {
+		return {
+			code: `module.exports = ${ JSON.stringify( path.basename( sourcePath ) ) };`,
+		};
+	},
+};

client/state/test/initial-state.js

@@ -3,7 +3,7 @@
  */
 
 import { withStorageKey } from '@automattic/state-utils';
-import * as browserStorage from 'calypso/lib/browser-storage';
+import * as browserStorageMethods from 'calypso/lib/browser-storage';
 import { isSupportSession } from 'calypso/lib/user/support-user-interop';
 import { createReduxStore } from 'calypso/state';
 import { addReducerToStore } from 'calypso/state/add-reducer';
@@ -27,6 +27,9 @@ const initialReducer = combineReducers( {
 	postTypes,
 } );
 
+// Needed to be able to mock browserStorage later
+const browserStorage = { ...browserStorageMethods };
+
 jest.mock( 'calypso/lib/user/support-user-interop', () => ( {
 	isSupportSession: jest.fn().mockReturnValue( false ),
 } ) );
@@ -1000,6 +1003,7 @@ describe( 'loading stored state with dynamic reducers', () => {
 
 		// load initial state and create Redux store with it
 		await loadPersistedState();
+
 		const userId = 123456789;
 		const state = getInitialState( reducer, userId );
 		const store = createReduxStore( state, reducer );

package.json

@@ -222,6 +222,8 @@
 		"@signal-noise/stylelint-scales": "^2.0.3",
 		"@storybook/cli": "^7.5.2",
 		"@storybook/react": "^7.5.2",
+		"@swc/core": "^1.3.96",
+		"@swc/jest": "^0.2.29",
 		"@tanstack/eslint-plugin-query": "^4.29.8",
 		"@testing-library/jest-dom": "^6.1.4",
 		"@types/gradient-parser": "^0.1.4",

test/client/jest.config.js

@@ -6,10 +6,33 @@ module.exports = {
 	rootDir: '../../client',
 	cacheDirectory: path.join( __dirname, '../../.cache/jest' ),
 	testPathIgnorePatterns: [ '<rootDir>/server/' ],
-
 	moduleNameMapper: {
 		'^@automattic/calypso-config$': '<rootDir>/server/config/index.js',
 	},
+	transform: {
+		'\\.(css|scss|jpg|jpeg|png|gif|eot|otf|webp|svg|ttf|woff|woff2|mp4|webm|wav|mp3|m4a|aac|oga)$':
+			'<rootDir>/__mocks__/file-transformer.js',
+		'^.+\\.(t|j)sx?$': [
+			'@swc/jest',
+			{
+				jsc: {
+					parser: {
+						syntax: 'typescript',
+						tsx: true,
+					},
+					transform: {
+						react: {
+							runtime: 'automatic',
+						},
+					},
+				},
+				env: {
+					mode: 'entry',
+					coreJs: '3.33.2',
+				},
+			},
+		],
+	},
 	transformIgnorePatterns: [
 		'node_modules[\\/\\\\](?!.*\\.(?:gif|jpg|jpeg|png|svg|scss|sass|css)$)',
 	],

yarn.lock

@@ -4349,6 +4349,15 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@jest/create-cache-key-function@npm:^27.4.2":
+  version: 27.5.1
+  resolution: "@jest/create-cache-key-function@npm:27.5.1"
+  dependencies:
+    "@jest/types": ^27.5.1
+  checksum: 1890ac93fad852e0a98c31de1e5f2c548974aefd36e838d27b70834dda1654a153ed6a52258447ebacfd47463e9bdb83750631bee827797c7b9973c083998a96
+  languageName: node
+  linkType: hard
+
 "@jest/environment@npm:^29.7.0":
   version: 29.7.0
   resolution: "@jest/environment@npm:29.7.0"
@@ -4510,6 +4519,19 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@jest/types@npm:^27.5.1":
+  version: 27.5.1
+  resolution: "@jest/types@npm:27.5.1"
+  dependencies:
+    "@types/istanbul-lib-coverage": ^2.0.0
+    "@types/istanbul-reports": ^3.0.0
+    "@types/node": "*"
+    "@types/yargs": ^16.0.0
+    chalk: ^4.0.0
+  checksum: 4598b302398db0eb77168b75a6c58148ea02cc9b9f21c5d1bbe985c1c9257110a5653cf7b901c3cab87fba231e3fed83633687f1c0903b4bc6939ab2a8452504
+  languageName: node
+  linkType: hard
+
 "@jest/types@npm:^29.5.0, @jest/types@npm:^29.6.3":
   version: 29.6.3
   resolution: "@jest/types@npm:29.6.3"
@@ -7061,7 +7083,7 @@ __metadata:
   languageName: node
   linkType: hard
 
-"@swc/core@npm:^1.3.82":
+"@swc/core@npm:^1.3.82, @swc/core@npm:^1.3.96":
   version: 1.3.96
   resolution: "@swc/core@npm:1.3.96"
   dependencies:
@@ -7114,6 +7136,18 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@swc/jest@npm:^0.2.29":
+  version: 0.2.29
+  resolution: "@swc/jest@npm:0.2.29"
+  dependencies:
+    "@jest/create-cache-key-function": ^27.4.2
+    jsonc-parser: ^3.2.0
+  peerDependencies:
+    "@swc/core": "*"
+  checksum: 10f34341f9bc8003cec44f91a88b531ba44094aad97b2f8410fb2f94db9eb3b8fc7f6d14ba867eb9c1dc6ba29cc46058244b8280d673a7c681062fe0dc73c3f0
+  languageName: node
+  linkType: hard
+
 "@swc/types@npm:^0.1.5":
   version: 0.1.5
   resolution: "@swc/types@npm:0.1.5"
@@ -8356,6 +8390,15 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@types/yargs@npm:^16.0.0":
+  version: 16.0.8
+  resolution: "@types/yargs@npm:16.0.8"
+  dependencies:
+    "@types/yargs-parser": "*"
+  checksum: ba659eb5a48009ccaa8d6426ad63f2b8de09c153d02f70c911d86b421cfc29ad63e92e17c120d97e81f43cda306760fb3cb5a4137b083d5fafb38c174a6ddf01
+  languageName: node
+  linkType: hard
+
 "@types/yargs@npm:^17.0.1, @types/yargs@npm:^17.0.8":
   version: 17.0.24
   resolution: "@types/yargs@npm:17.0.24"
@@ -32247,6 +32290,8 @@ __metadata:
     "@signal-noise/stylelint-scales": ^2.0.3
     "@storybook/cli": ^7.5.2
     "@storybook/react": ^7.5.2
+    "@swc/core": ^1.3.96
+    "@swc/jest": ^0.2.29
     "@tanstack/eslint-plugin-query": ^4.29.8
     "@testing-library/jest-dom": ^6.1.4
     "@types/cookie": ^0.4.1