refactor(gateway): restructure gateway with new dependency injection and services

Reorganize app/gateway/ with:
- common/ - lifespan management
- dependencies/ - FastAPI dependency injection (db, checkpointer, repositories, stream_bridge)
- services/runs/ - run execution services (facade_factory, input adapters, store operations)
- registrar.py - router registration
- router.py - main router setup

Simplify app.py to use the new modular structure.
Remove deprecated utils.py.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/gateway/dependencies/__init__.py

@@ -0,0 +1,59 @@
+from app.gateway.dependencies.checkpointer import (
+    CurrentCheckpointer,
+    get_checkpointer,
+)
+from app.plugins.auth.security.dependencies import (
+    CurrentAuthService,
+    CurrentUserRepository,
+    get_auth_service,
+    get_current_user_from_request,
+    get_current_user_id,
+    get_optional_user_from_request,
+    get_user_repository,
+)
+from app.gateway.dependencies.db import (
+    CurrentSession,
+    CurrentSessionTransaction,
+    get_db_session,
+    get_db_session_transaction,
+)
+from app.gateway.dependencies.repositories import (
+    CurrentFeedbackRepository,
+    CurrentRunRepository,
+    CurrentThreadMetaRepository,
+    CurrentThreadMetaStorage,
+    get_feedback_repository,
+    get_run_repository,
+    get_thread_meta_repository,
+    get_thread_meta_storage,
+)
+from app.gateway.dependencies.stream_bridge import (
+    CurrentStreamBridge,
+    get_stream_bridge,
+)
+
+__all__ = [
+    "CurrentCheckpointer",
+    "CurrentAuthService",
+    "CurrentFeedbackRepository",
+    "CurrentRunRepository",
+    "CurrentSession",
+    "CurrentSessionTransaction",
+    "CurrentStreamBridge",
+    "CurrentThreadMetaRepository",
+    "CurrentThreadMetaStorage",
+    "CurrentUserRepository",
+    "get_auth_service",
+    "get_checkpointer",
+    "get_current_user_from_request",
+    "get_current_user_id",
+    "get_db_session",
+    "get_db_session_transaction",
+    "get_feedback_repository",
+    "get_optional_user_from_request",
+    "get_run_repository",
+    "get_stream_bridge",
+    "get_thread_meta_repository",
+    "get_thread_meta_storage",
+    "get_user_repository",
+]