feat: add support for allowed_web_search_modes in requirements.toml

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.

codex-rs/app-server/src/config_api.rs

@@ -17,6 +17,7 @@ use codex_core::config_loader::ConfigRequirementsToml;
 use codex_core::config_loader::LoaderOverrides;
 use codex_core::config_loader::ResidencyRequirement as CoreResidencyRequirement;
 use codex_core::config_loader::SandboxModeRequirement as CoreSandboxModeRequirement;
+use codex_protocol::config_types::WebSearchMode;
 use serde_json::json;
 use std::path::PathBuf;
 use std::sync::Arc;
@@ -115,6 +116,16 @@ fn map_requirements_toml_to_api(requirements: ConfigRequirementsToml) -> ConfigR
                 .filter_map(map_sandbox_mode_requirement_to_api)
                 .collect()
         }),
+        allowed_web_search_modes: requirements.allowed_web_search_modes.map(|modes| {
+            let mut normalized = modes
+                .into_iter()
+                .map(Into::into)
+                .collect::<Vec<WebSearchMode>>();
+            if !normalized.contains(&WebSearchMode::Disabled) {
+                normalized.push(WebSearchMode::Disabled);
+            }
+            normalized
+        }),
         enforce_residency: requirements
             .enforce_residency
             .map(map_residency_requirement_to_api),
@@ -177,6 +188,9 @@ mod tests {
                 CoreSandboxModeRequirement::ReadOnly,
                 CoreSandboxModeRequirement::ExternalSandbox,
             ]),
+            allowed_web_search_modes: Some(vec![
+                codex_core::config_loader::WebSearchModeRequirement::Cached,
+            ]),
             mcp_servers: None,
             rules: None,
             enforce_residency: Some(CoreResidencyRequirement::Us),
@@ -195,9 +209,32 @@ mod tests {
             mapped.allowed_sandbox_modes,
             Some(vec![SandboxMode::ReadOnly]),
         );
+        assert_eq!(
+            mapped.allowed_web_search_modes,
+            Some(vec![WebSearchMode::Cached, WebSearchMode::Disabled]),
+        );
         assert_eq!(
             mapped.enforce_residency,
             Some(codex_app_server_protocol::ResidencyRequirement::Us),
         );
     }
+
+    #[test]
+    fn map_requirements_toml_to_api_normalizes_allowed_web_search_modes() {
+        let requirements = ConfigRequirementsToml {
+            allowed_approval_policies: None,
+            allowed_sandbox_modes: None,
+            allowed_web_search_modes: Some(Vec::new()),
+            mcp_servers: None,
+            rules: None,
+            enforce_residency: None,
+        };
+
+        let mapped = map_requirements_toml_to_api(requirements);
+
+        assert_eq!(
+            mapped.allowed_web_search_modes,
+            Some(vec![WebSearchMode::Disabled])
+        );
+    }
 }