[Bug]: Browse E2E does not verify native file selection

Describe the bug

The winapp.sign Browse E2E smoke test only verifies that the QuickPick disappears and no immediate error notification appears. It does not prove that the native Open dialog was shown, that a selected path returns to the extension, or that the selected file reaches the signing flow. The existing Playwright path cannot interact with native Windows dialogs and is also timing-sensitive.

To Reproduce

1. Run the Browse test in src/test/e2e/sign-quickpick.spec.ts.
2. Observe that its assertions stop after QuickPick dismissal.
3. A regression that dismisses the QuickPick without opening/handling the native dialog can still satisfy the assertions.

Expected behavior

Use the repository's UI Automation/driver-queue harness or an injectable picker adapter to verify that choosing Browse opens the native dialog and returns the selected file into the sign flow.

Screenshots

N/A

OS Version and details

Windows

Start with src/test/e2e/sign-quickpick.spec.ts and inspect the repository's UI Automation/driver-queue harness or picker adapter. Trace the Browse action through the native Open dialog and back into the extension's signing flow. Done means the test verifies the dialog opens, a selected path returns, and that path reaches signing rather than only checking QuickPick dismissal.