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/app-server/src/request_processors/thread_processor.rs

@@ -1239,17 +1239,18 @@ impl ThreadRequestProcessor {
         approval_policy: Option<codex_app_server_protocol::AskForApproval>,
         approvals_reviewer: Option<codex_app_server_protocol::ApprovalsReviewer>,
         sandbox: Option<SandboxMode>,
-        permissions: Option<PermissionProfileSelectionParams>,
+        permissions: Option<String>,
         base_instructions: Option<String>,
         developer_instructions: Option<String>,
         personality: Option<Personality>,
     ) -> ConfigOverrides {
-        let mut overrides = ConfigOverrides {
+        ConfigOverrides {
             model,
             model_provider,
             service_tier,
             cwd: cwd.map(PathBuf::from),
             workspace_roots: runtime_workspace_roots,
+            default_permissions: permissions,
             approval_policy: approval_policy
                 .map(codex_app_server_protocol::AskForApproval::to_core),
             approvals_reviewer: approvals_reviewer
@@ -1261,9 +1262,7 @@ impl ThreadRequestProcessor {
             developer_instructions,
             personality,
             ..Default::default()
-        };
-        apply_permission_profile_selection_to_config_overrides(&mut overrides, permissions);
-        overrides
+        }
     }
 
     fn parse_environment_selections(