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/tui/src/app/thread_session_state.rs

@@ -123,16 +123,15 @@ mod tests {
     use crate::test_support::PathBufExt;
     use crate::test_support::test_path_buf;
     use codex_app_server_protocol::AskForApproval;
-    use codex_app_server_protocol::FileSystemAccessMode;
-    use codex_app_server_protocol::FileSystemPath;
-    use codex_app_server_protocol::FileSystemSandboxEntry;
-    use codex_app_server_protocol::FileSystemSpecialPath;
-    use codex_app_server_protocol::PermissionProfile as AppServerPermissionProfile;
-    use codex_app_server_protocol::PermissionProfileFileSystemPermissions;
-    use codex_app_server_protocol::PermissionProfileNetworkPermissions;
     use codex_config::types::ApprovalsReviewer;
     use codex_protocol::models::BUILT_IN_PERMISSION_PROFILE_WORKSPACE;
+    use codex_protocol::models::ManagedFileSystemPermissions;
     use codex_protocol::models::PermissionProfile;
+    use codex_protocol::permissions::FileSystemAccessMode;
+    use codex_protocol::permissions::FileSystemPath;
+    use codex_protocol::permissions::FileSystemSandboxEntry;
+    use codex_protocol::permissions::FileSystemSpecialPath;
+    use codex_protocol::permissions::NetworkSandboxPolicy;
     use pretty_assertions::assert_eq;
     use std::path::PathBuf;
 
@@ -255,9 +254,9 @@ mod tests {
         let mut app = make_test_app().await;
         let thread_id =
             ThreadId::from_string("00000000-0000-0000-0000-000000000403").expect("valid thread");
-        let profile: PermissionProfile = AppServerPermissionProfile::Managed {
-            network: PermissionProfileNetworkPermissions { enabled: false },
-            file_system: PermissionProfileFileSystemPermissions::Restricted {
+        let profile: PermissionProfile = PermissionProfile::Managed {
+            network: NetworkSandboxPolicy::Restricted,
+            file_system: ManagedFileSystemPermissions::Restricted {
                 entries: vec![
                     FileSystemSandboxEntry {
                         path: FileSystemPath::Special {
@@ -274,8 +273,7 @@ mod tests {
                 ],
                 glob_scan_max_depth: None,
             },
-        }
-        .into();
+        };
         let session = ThreadSessionState {
             permission_profile: profile.clone(),
             ..test_thread_session(thread_id, test_path_buf("/tmp/main"))