app-server-protocol: remove PermissionProfile from API (#22924)

## Why

The app server API should expose permission profile identity, not the
lower-level runtime permission model. `PermissionProfile` is the
compiled sandbox/network representation that the server uses internally;
exposing it through app-server-protocol forces clients to understand
details that should remain implementation-level.

The API boundary should prefer `ActivePermissionProfile`: a stable
profile id, plus future parent-profile metadata, that clients can pass
back when they want to select the same active permissions. This also
avoids schema generation collisions between the app-server v2 API type
space and the core protocol model.

Incidentally, while PR makes a number of changes to `command/exec`, note
that we are hoping to deprecate this API in favor of `process/spawn`, so
we don't need to be too finicky about these changes.

## What Changed

- Removed `PermissionProfile` from the app-server-protocol API surface,
including generated schema and TypeScript exports.
- Changed `CommandExecParams.permissionProfile` to
`ActivePermissionProfile`.
- Resolve command exec profile ids through `ConfigManager` for the
command cwd, matching turn override selection semantics.
- Updated downstream TUI tests/helpers to use core permission types
directly instead of app-server-protocol `PermissionProfile` shims.

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

@@ -1,4 +1,4 @@
-use super::PermissionProfile;
+use super::ActivePermissionProfile;
 use super::SandboxPolicy;
 use codex_experimental_api_macros::ExperimentalApi;
 use schemars::JsonSchema;
@@ -100,13 +100,13 @@ pub struct CommandExecParams {
     /// combined with `permissionProfile`.
     #[ts(optional = nullable)]
     pub sandbox_policy: Option<SandboxPolicy>,
-    /// Optional full permissions profile for this command.
+    /// Optional active permissions profile 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<PermissionProfile>,
+    pub permission_profile: Option<ActivePermissionProfile>,
 }
 
 /// Final buffered result for `command/exec`.