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/db.py

@@ -0,0 +1,37 @@
+from __future__ import annotations
+
+from collections.abc import AsyncIterator
+from typing import Annotated
+
+from fastapi import Depends, HTTPException, Request
+from sqlalchemy.ext.asyncio import AsyncSession, async_sessionmaker
+
+
+def _get_session_factory(request: Request) -> async_sessionmaker[AsyncSession]:
+    factory = getattr(request.app.state.persistence, "session_factory", None)
+    if factory is None:
+        raise HTTPException(status_code=503, detail="Database session factory not available")
+    return factory
+
+
+async def get_db_session(request: Request) -> AsyncIterator[AsyncSession]:
+    """Open a session without auto-commit. Use for read-only endpoints."""
+    session_factory = _get_session_factory(request)
+    async with session_factory() as session:
+        yield session
+
+
+async def get_db_session_transaction(request: Request) -> AsyncIterator[AsyncSession]:
+    """Open a session and commit on success, rollback on error."""
+    session_factory = _get_session_factory(request)
+    async with session_factory() as session:
+        try:
+            yield session
+            await session.commit()
+        except Exception:
+            await session.rollback()
+            raise
+
+
+CurrentSession = Annotated[AsyncSession, Depends(get_db_session)]
+CurrentSessionTransaction = Annotated[AsyncSession, Depends(get_db_session_transaction)]