## Why
The TUI unconditionally forwarded its resolved `web_search` mode, allowing implicit client settings to replace server defaults or saved thread settings.
## What changed
- Forward `web_search` on thread start, resume, and fork only when the winning choice comes from session flags or a selected profile.
- Translate legacy search feature flags into a canonical `web_search` override while preserving precedence, and remove those flags from forwarded feature overrides.
- Honor shared feature requirements for embedded sessions while letting remote servers enforce their own requirements on explicit search choices.
## Testing
Add coverage for configuration origins, canonical and legacy search precedence, and embedded versus remote feature requirements. Extend the Responses integration test to verify that a remote server's live search setting survives thread start and resume when the client's configuration disables search.
GitOrigin-RevId: c714f9cf0321aca9a5fa292a350720af5a2d02d4
Eric Traut
606b139565