## Why
The standalone `/v1/alpha/search` request now requires a `model`, but
the `web.run` extension currently omits it.
Adds `model` to extension `ToolCall` invocation.
Follow-up to #23823.
## What changed
- Make `SearchRequest.model` required.
- Expose the effective per-turn model on extension tool calls and pass
it in standalone web-search requests.
- Assert the model is forwarded in the app-server round-trip test.
## Testing
- `just test -p codex-api -p codex-tools -p codex-web-search-extension
-p codex-memories-extension -p codex-goal-extension`
- `just test -p codex-core -E
'test(passes_turn_fields_and_scoped_turn_item_emitter_to_extension_call)'`
- `just test -p codex-app-server -E
'test(standalone_web_search_round_trips_encrypted_output)'`
add standalone web search request types and a `codex-api` client ahead
of the extension-contributed search tool.
this adds typed commands/settings and opaque encrypted output handling
for the new standalone search flow. the endpoint types are close to
finalized but may still shift slightly as that API settles.
sayan-oai