Handle Windows browser-helper stdout exit races

The Windows browser helper can lose its final stdout payload during process exit. Reimplement the bounded stdout handoff after deterministic Windows reproduction. Source PR https://github.com/stablyai/orca/pull/11236; credit the PR author. No contributor action requested.

Start with source PR https://github.com/stablyai/orca/pull/11236 and reproduce the Windows browser-helper exit race deterministically. Then inspect the existing bounded stdout handoff and verify that the final stdout payload is preserved during process exit; the issue does not name specific files or tests.

Written by the indexing model from the issue text.