[Bug]: MCP browser_navigate blocks for the whole navigation timeout when the page opens a dialog during load

Version

1.64.0-next (main @ 07f1a6154)

Steps to reproduce

Serve a page that opens a dialog while loading:

<title>T</title><script>alert('hi')</script><h1>Hi</h1>

Then, with a default MCP server (Chromium):

1. browser_navigate { url: "http://localhost:PORT/" }
2. browser_snapshot {}

Repro with the repo's MCP fixtures and timeouts: { navigation: 3000 } to keep it short:

NAV after 4600 ms: ### Error
TimeoutError: browserBackend.callTool: Timeout 3000ms exceeded.
Call log:
  - navigating to "http://localhost:PORT/", waiting until "domcontentloaded"

SNAP= ### Error
Error: Tool "browser_snapshot" does not handle the modal state.
### Modal state
- ["alert" dialog with message "hi"]: can be handled by browser_handle_dialog

Expected behavior

browser_navigate returns as soon as the dialog opens and reports it in the modal state, the same way browser_click does when a click opens a dialog (see alert dialog w/ race in tests/mcp/dialogs.spec.ts). The agent can then call browser_handle_dialog and continue.

Actual behavior

page.goto never reaches domcontentloaded while the dialog is open, so the call blocks for the full navigation timeout (60s by default) and then fails with a TimeoutError. Only after that does the modal state become visible. With the default timeout this is long enough to trip client-side tool timeouts, and one hostile or buggy page stalls the whole server for a minute per navigation.

Additional context

Tab.navigate() (packages/playwright-core/src/tools/backend/tab.ts) awaits page.goto directly, while other actions go through waitForCompletion, which races the action against TabEvents.modalState (_raceAgainstModalStates). Navigation should use the same race, returning early when a modal state appears.

I intend to work on this and will send a PR.

Environment

- Operating System: macOS (Darwin 25.6.0)
- Node.js: 24.8.0
- Browser: Chromium
- Playwright: main @ 07f1a6154