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/checkpointer.py

@@ -0,0 +1,20 @@
+from __future__ import annotations
+
+from typing import Annotated
+
+from fastapi import Depends, HTTPException, Request
+from langgraph.types import Checkpointer
+
+
+def get_checkpointer(request: Request) -> Checkpointer:
+    """Get checkpointer from app.state.persistence."""
+    persistence = getattr(request.app.state, "persistence", None)
+    if persistence is None:
+        raise HTTPException(status_code=503, detail="Persistence not available")
+    checkpointer = getattr(persistence, "checkpointer", None)
+    if checkpointer is None:
+        raise HTTPException(status_code=503, detail="Checkpointer not available")
+    return checkpointer
+
+
+CurrentCheckpointer = Annotated[Checkpointer, Depends(get_checkpointer)]