app-server: use profile ids in v2 permission params (#23360)

## Why

The v2 app-server permission profile fields are experimental, but the
previous migration kept a legacy object payload for profile selection.
That made clients aware of server-owned `activePermissionProfile`
metadata such as `extends`, and it kept a
`legacy_additional_writable_roots` path even though
`runtimeWorkspaceRoots` now owns runtime workspace-root selection.

This PR makes the client contract match the intended model: clients
select a permission profile by id, and the server resolves and reports
active profile provenance in response payloads.

Follow-up to #22611.

## What Changed

- Changed `thread/start`, `thread/resume`, `thread/fork`, and
`turn/start` permission profile selection to plain profile id strings.
- Changed `command/exec.permissionProfile` to a plain profile id string
for the same client/server ownership split.
- Removed `PermissionProfileSelectionParams` and the legacy `{ type:
"profile", modifications: [...] }` compatibility deserializer.
- Updated app-server, TUI, and `codex exec` call sites to send only ids,
while keeping `activePermissionProfile` as server response metadata.
- Updated app-server docs and schema fixtures for the revised
`command/exec.permissionProfile` shape.

## Verification

- `cargo test -p codex-app-server-protocol`
- `RUST_MIN_STACK=8388608 cargo test -p codex-app-server`
- `cargo test -p codex-exec`
- `RUST_MIN_STACK=8388608 cargo test -p codex-tui`

---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/23360).
* #23368
* __->__ #23360

codex-rs/exec/src/lib.rs

@@ -24,7 +24,6 @@ use codex_app_server_protocol::ConfigWarningNotification;
 use codex_app_server_protocol::JSONRPCErrorError;
 use codex_app_server_protocol::McpServerElicitationAction;
 use codex_app_server_protocol::McpServerElicitationRequestResponse;
-use codex_app_server_protocol::PermissionProfileSelectionParams;
 use codex_app_server_protocol::RequestId;
 use codex_app_server_protocol::ReviewStartParams;
 use codex_app_server_protocol::ReviewStartResponse;
@@ -1009,17 +1008,15 @@ fn thread_resume_params_from_config(config: &Config, thread_id: String) -> Threa
     }
 }
 
-fn permissions_selection_from_config(config: &Config) -> Option<PermissionProfileSelectionParams> {
+fn permissions_selection_from_config(config: &Config) -> Option<String> {
     config
         .permissions
         .active_permission_profile()
-        .map(permissions_selection_from_active_profile)
+        .map(permission_profile_id_from_active_profile)
 }
 
-fn permissions_selection_from_active_profile(
-    active: ActivePermissionProfile,
-) -> PermissionProfileSelectionParams {
-    PermissionProfileSelectionParams::new(active.id)
+fn permission_profile_id_from_active_profile(active: ActivePermissionProfile) -> String {
+    active.id
 }
 
 fn sandbox_mode_from_permission_profile(

codex-rs/exec/src/lib_tests.rs

@@ -479,14 +479,11 @@ async fn thread_start_params_include_user_thread_source() {
 
 #[test]
 fn active_profile_selection_uses_profile_id_only() {
-    let selection = permissions_selection_from_active_profile(ActivePermissionProfile::new(
+    let selection = permission_profile_id_from_active_profile(ActivePermissionProfile::new(
         BUILT_IN_PERMISSION_PROFILE_WORKSPACE,
     ));
 
-    assert_eq!(
-        selection,
-        PermissionProfileSelectionParams::new(BUILT_IN_PERMISSION_PROFILE_WORKSPACE)
-    );
+    assert_eq!(selection, BUILT_IN_PERMISSION_PROFILE_WORKSPACE.to_string());
 }
 
 #[tokio::test]