## 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)'`
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