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/__init__.py

@@ -1,4 +1,23 @@
-from .app import app, create_app
-from .config import GatewayConfig, get_gateway_config
+from __future__ import annotations
 
-__all__ = ["app", "create_app", "GatewayConfig", "get_gateway_config"]
+__all__ = ["GatewayConfig", "app", "get_gateway_config", "register_app"]
+
+
+def __getattr__(name: str):
+    if name == "app":
+        from .app import app
+
+        return app
+    if name == "GatewayConfig":
+        from .config import GatewayConfig
+
+        return GatewayConfig
+    if name == "get_gateway_config":
+        from .config import get_gateway_config
+
+        return get_gateway_config
+    if name == "register_app":
+        from .registrar import register_app
+
+        return register_app
+    raise AttributeError(name)