Upgrade @playwright/test and cleanup internal APIs (#77659)

Addressing the API incompatibility in the newest Playwright release:
microsoft/playwright#27059 (comment)

cc @wyozi

Author: dvoytenko

packages/next/package.json

@@ -110,7 +110,7 @@
   },
   "peerDependencies": {
     "@opentelemetry/api": "^1.1.0",
-    "@playwright/test": "^1.41.2",
+    "@playwright/test": "^1.51.1",
     "babel-plugin-react-compiler": "*",
     "react": "^18.2.0 || 19.0.0-rc-de68d2f4-20241204 || ^19.0.0",
     "react-dom": "^18.2.0 || 19.0.0-rc-de68d2f4-20241204 || ^19.0.0",
@@ -170,7 +170,7 @@
     "@next/react-refresh-utils": "15.3.0-canary.26",
     "@next/swc": "15.3.0-canary.26",
     "@opentelemetry/api": "1.6.0",
-    "@playwright/test": "1.41.2",
+    "@playwright/test": "1.51.1",
     "@storybook/addon-a11y": "8.6.0",
     "@storybook/addon-essentials": "8.6.0",
     "@storybook/addon-interactions": "8.6.0",

packages/next/src/experimental/testmode/playwright/step.ts

@@ -9,33 +9,13 @@ export interface StepProps {
   params?: Record<string, string | number | boolean | null | undefined>
 }
 
-// Access the internal Playwright API until it's exposed publicly.
-// See https://github.com/microsoft/playwright/issues/27059.
-interface TestInfoWithRunAsStep extends TestInfo {
-  _runAsStep: <T>(
-    stepInfo: StepProps,
-    handler: (result: { complete: Complete }) => Promise<T>
-  ) => Promise<T>
-}
-
 type Complete = (result: { error?: any }) => void
 
-function isWithRunAsStep(
-  testInfo: TestInfo
-): testInfo is TestInfoWithRunAsStep {
-  return '_runAsStep' in testInfo
-}
-
 export async function step<T>(
-  testInfo: TestInfo,
+  _testInfo: TestInfo,
   props: StepProps,
   handler: (complete: Complete) => Promise<Awaited<T>>
 ): Promise<Awaited<T>> {
-  if (isWithRunAsStep(testInfo)) {
-    return testInfo._runAsStep(props, ({ complete }) => handler(complete))
-  }
-
-  // Fallback to the `test.step()`.
   let result: Awaited<T>
   let reportedError: any
   try {