Example:
```toml
# This means that "live" is not allowed; "disabled" is allowed even though not listed explicitly.
allowed_web_search_modes = ["cached"]
```
### Why
- Support admin/MDM/requirements.toml constraints over web-search behavior, independent of user config or sandbox defaults.
- Ensure per-turn config resolution and review-mode overrides can never crash when constraints are present.
- Note that `allowed_web_search_modes = ["cached"]` denies `"live"`, even if `--yolo` is used. See `resolve_web_search_mode_for_turn()`.
### What
- Add `allowed_web_search_modes` to requirements parsing and app-server v2 `ConfigRequirements` (`allowedWebSearchModes`), with schema/TS fixture updates.
- Introduce TOML-only `WebSearchModeRequirement` for requirements allowlists; accept `disabled|cached|live`, and treat an empty list as `[disabled]`.
- Convert the allowlist to a `ConstrainedWithSource<Option<WebSearchMode>>`, always permitting `Disabled` while enforcing membership for other values.
- Make `Config.web_search_mode` a constrained field, update call sites/tests, and surface constraint violations via warnings/fallback.
- Extend TUI `/debug-config` output to display `allowed_web_search_modes`.
### Safety
- Avoid `expect()` on constrained `web_search_mode` mutation in session per-turn config and review-thread setup; warn and keep the constrained value instead.
Similar to what @sayan-oai did in openai/codex#8956 for
`config.schema.json`, this PR updates the repo so that it includes the
output of `codex app-server generate-json-schema` and `codex app-server
generate-ts` and adds a test to verify it is in sync with the current
code.
Motivation:
- This makes any schema changes introduced by a PR transparent during
code review.
- In particular, this should help us catch PRs that would introduce a
non-backwards-compatible change to the app schema (eventually, this
should also be enforced by tooling).
- Once https://github.com/openai/codex/pull/10231 is in to formalize the
notion of "experimental" fields, we can work on ensuring the
non-experimental bits are backwards-compatible.
`codex-rs/app-server-protocol/tests/schema_fixtures.rs` was added as the
test and `just write-app-server-schema` can be use to generate the
vendored schema files.
Incidentally, when I run:
```
rg _ codex-rs/app-server-protocol/schema/typescript/v2
```
I see a number of `snake_case` names that should be `camelCase`.
