[Bug]: Ensure patched node-pty native rebuilds actually run across package-manager versions

## Summary

The native build path can report success while `pnpm rebuild` does not rebuild the patched `node-pty` artifact, leaving stale or missing native binaries. The owner path should invoke the supported node-gyp rebuild directly (or an equivalent verified command) and validate the resulting artifact across package-manager versions and platforms.

## Source PR

- #11754 — rebuild patched node-pty via node-gyp instead of relying on `pnpm rebuild` (credit @Gldywn)

This issue is paired with #16655 for standalone-pnpm dispatch, but tracks the distinct rebuild-execution guarantee. The submitted branch will be superseded and reimplemented on current main; no contributor action is requested.