Add experimental app-server project APIs (#38940)

## What changed

- Add SQLite-backed `project/list`, `project/read`, `project/create`,
  `project/import`, `project/update`, `project/move`, and `project/delete`
  endpoints with ordered roots, metadata, manual positioning, pagination, and
  idempotent creation.
- Add project assignment to thread start, metadata updates, list filtering,
  and fork inheritance. Project deletion clears assignments without deleting
  threads.
- Emit `project/changed` and `thread/project/updated` notifications after
  committed changes, and export the new protocol schemas and TypeScript types.

## Testing

- Cover project lifecycle and ordering, idempotency, atomic imports, cursor and
  filter validation, thread assignment, deletion, and fork inheritance.

GitOrigin-RevId: 47ae621be01ab8ef70a74a629fb29a5c5709ea33

codex-rs/thread-store/src/lib.rs

@@ -8,6 +8,7 @@ mod error;
 mod in_memory;
 mod live_thread;
 mod local;
+mod projects;
 mod queue_store;
 mod store;
 mod thread_metadata_sync;
@@ -30,6 +31,17 @@ pub use local::RolloutMigrationOutcome;
 pub use local::RolloutMigrationProgress;
 pub use local::RolloutMigrationReport;
 pub use local::RolloutMigrationStatus;
+pub use projects::CreateProjectParams;
+pub use projects::CreatedProject;
+pub use projects::DeletedProject;
+pub use projects::ListProjectsParams;
+pub use projects::MoveProjectParams;
+pub use projects::ProjectMoveOutcome;
+pub use projects::StoredProject;
+pub use projects::StoredProjectRoot;
+pub use projects::StoredProjectsPage;
+pub use projects::UpdateProjectParams;
+pub use projects::UpdatedProject;
 pub use queue_store::LocalQueueStore;
 pub use queue_store::QueueStore;
 pub use store::PersistContext;