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)
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with [ReviewStack](https://reviewstack.dev/openai/codex/pull/23360).
* #23368
* __->__ #23360

codex-rs/app-server-protocol/src/protocol/v2/command_exec.rs

@@ -1,4 +1,3 @@
-use super::ActivePermissionProfile;
 use super::SandboxPolicy;
 use codex_experimental_api_macros::ExperimentalApi;
 use schemars::JsonSchema;
@@ -100,13 +99,13 @@ pub struct CommandExecParams {
     /// combined with `permissionProfile`.
     #[ts(optional = nullable)]
     pub sandbox_policy: Option<SandboxPolicy>,
-    /// Optional active permissions profile for this command.
+    /// Optional active permissions profile id for this command.
     ///
     /// Defaults to the user's configured permissions when omitted. Cannot be
     /// combined with `sandboxPolicy`.
     #[experimental("command/exec.permissionProfile")]
     #[ts(optional = nullable)]
-    pub permission_profile: Option<ActivePermissionProfile>,
+    pub permission_profile: Option<String>,
 }
 
 /// Final buffered result for `command/exec`.