# why

Expose browser-side predicate waiting consistently across Stagehand
SDKs, without transport polling.

This is PR2 of 2, stacked directly on #3179
(`amel/wait-for-function-extension`). Polling, navigation recovery, and
cleanup live in the parent; merge it first using the repository’s
stacked-PR handoff rules.

# what changed

- Register `page.wait_for_function` and connect the extension
controller/runtime to the internal implementation.
- Add TypeScript `waitForFunction(expression, arg?, options?)`, Python
`wait_for_function(expression, *, arg, polling, timeout)`, and Go
`WaitForFunction`. As in Playwright, an expression that evaluates to a
function is invoked on each poll and receives the optional JSON `arg`.
- Preserve JSON result keys through opaque wire metadata, with roundtrip
coverage for own `toString`, `constructor`, and `hasOwnProperty` keys in
nested payloads. No browser-handle API is introduced.
- Provide RAF/interval polling and no deadline by default in all three
SDKs; pass `timeout` to bound a wait. An omitted or zero timeout also
drops the client response deadline.
- Derive internal wait options from the canonical protocol contract.
Reuse the TypeScript argument serializer. Model Go’s string-or-number
polling option through its existing typed-union generator extension
point.
- Regenerate protocol/models/final ZIP and include docs plus minor
release entries for all five packages.

Reviewed with the requested Thermo-Nuclear Code Quality Review skill,
including an independent cross-review of SDK boundaries. No SDK polling
loops, duplicated serializer, broad generator abstraction, or new
1,000-line file crossing.

# test plan

- 9 real-Chrome tests passed, including main-world access, async
predicates, custom intervals, error propagation, navigation recovery,
concurrent waits, and timeout-zero closure.
- 79 extension/selector tests and 788 protocol/docs/SDK/architecture
guards passed.
- 184 Python tests plus Ruff/type checks passed; Go SDK package tests
passed.
- Follow-up review: 26 wire tests passed; canonical option types emit
unchanged JavaScript, and the rebuilt extension ZIP remains identical.
- Extension/SDK/protocol typechecks, dependency-ordered build,
generated-model/ZIP checks, formatting, lint, and `git diff --check`
passed.

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Co-authored-by: miguel <miguelg71921@gmail.com>