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/services/runs/__init__.py

@@ -0,0 +1,29 @@
+"""Runs app layer services."""
+
+from app.infra.storage import StorageRunObserver
+from .input import (
+    AdaptedRunRequest,
+    RunSpecBuilder,
+    UnsupportedRunFeatureError,
+    adapt_create_run_request,
+    adapt_create_stream_request,
+    adapt_create_wait_request,
+    adapt_join_stream_request,
+    adapt_join_wait_request,
+)
+from .store import AppRunCreateStore, AppRunDeleteStore, AppRunQueryStore
+
+__all__ = [
+    "AdaptedRunRequest",
+    "AppRunCreateStore",
+    "AppRunDeleteStore",
+    "AppRunQueryStore",
+    "RunSpecBuilder",
+    "StorageRunObserver",
+    "UnsupportedRunFeatureError",
+    "adapt_create_run_request",
+    "adapt_create_stream_request",
+    "adapt_create_wait_request",
+    "adapt_join_stream_request",
+    "adapt_join_wait_request",
+]