## Summary
- add contains_external_context() to tool output so other tools can be
opted out of influencing memory when disable_on_external_context=true
- Classify standalone web-search output as external context (to match
behavior as hosted web search)
- Verify with integration test
## What
- Consume plaintext `output` from standalone search while retaining
optional `encrypted_output` parsing.
- Expose `web.run` to code mode and return search output to nested
JavaScript calls.
- Cover direct and code-mode standalone search paths with integration
tests.
## Why
`/v1/alpha/search` now returns plaintext output, which code mode needs
to consume standalone search results.
## Test plan
- `just test -p codex-api`
- `just test -p codex-web-search-extension`
- `just test -p codex-core code_mode_can_call_standalone_web_search`
- `just test -p codex-app-server
standalone_web_search_round_trips_output`
## Summary
Add the extension-backed standalone `web.run` tool so Codex can call the
standalone search endpoint through the `codex-api` search client and
return its encrypted output to Responses.
- gate the new tool behind `standalone_web_search`
- install the extension in the app-server thread registry and hide
hosted `web_search` when standalone search is enabled for OpenAI
providers so the two paths stay mutually exclusive
- build search context from persisted history using a small tail
heuristic: previous user message, assistant text between the last two
user turns capped at about 1k tokens, and current user message
## Test Plan
- `cargo test -p codex-web-search-extension`
- `cargo test -p codex-api`
- `cargo test -p codex-core
hosted_tools_follow_provider_auth_model_and_config_gates`
rka-oai