[microsoft-playwright-automation]

• Cache handler wrappers without writing attributes to user callables. Weak values release unused wrappers; identity-based keys support repeated bound-method lookups without retaining receivers or requiring hashable callables.
• Pass the supplied arguments to native callables that have no inspectable signature, such as set.add and set.__contains__. Other signature errors still propagate.
• Extend the existing sync console test to check built-in listeners, public wrapper objects, removal, and once.

Verified on Windows with Chromium, Firefox, and WebKit: 340 sync tests and 295 async tests passed, with existing skips and upstream xfails. Independent checks cover slotted/frozen handlers and native route predicates in both APIs. The pinned mypy and pyright pass with Linux platform definitions; their default Windows checks report existing POSIX-only API errors. Serial flake8, the remaining pre-commit hooks, generation consistency, and the test registry check passed.

Fixes #3340

_{Triaged on Windows by the Playwright bot - agent run}