[codex] Require model for standalone web search

[sayan-oai]

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)'

[jif-oai]

make sense