## Summary
- opt the extension-backed standalone `web.run` tool into parallel tool
execution
- update the existing extension registration test to assert that the
tool advertises parallel-call support
## Why
The standalone web-search API endpoint now supports parallel requests.
The extension executor still inherited the shared serial default,
causing multiple `web.run` calls to acquire the exclusive runtime lock.
## Impact
Models that emit multiple standalone web-search calls can now execute
them concurrently when model-level parallel tool calls are enabled.
## Validation
- `just fmt`
- `just test -p codex-web-search-extension`
- `git diff --check origin/main...HEAD`
## 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)'`
## Why
Standalone `web.run` calls run in the extension, so they need normal
web-search progress activity while a request is in flight and durable
completed activity after a thread is reloaded.
Follow-up to #23823; uses the extension turn-item emission path added in
#24813.
## What changed
- Emit standalone `web.run` start/completion items through the host
turn-item emitter, preserving standard client delivery and rollout
persistence.
- Include useful completion detail for queries, image queries, and
literal-URL `open`/`find` commands.
- Render completed searches as `Searched the web` or `Searched the web
for <detail>`, with snapshot coverage for the detail-free case.
- Extend the app-server round-trip test to verify completed search
activity is reconstructed by `thread/read` after a fresh-process reload.
## Testing
- `just test -p codex-web-search-extension`
- `just test -p codex-app-server -E
"test(standalone_web_search_round_trips_encrypted_output)"`
add new `parse_tool_input_schema_without_compaction` to bypass the
existing compaction/trimming of client-provided tool schemas that are
over 4k bytes.
we want this for standalone web search to keep field guidance/metadata
on certain fields; this keeps us closer to parity with existing hosted
tool schema (which didnt go through this 4k byte filter).
## 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`
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