fix: initialize MCP session_manager in lifespan and fix mount path

StreamableHTTPSessionManager requires its run() context manager to be
active before handling requests. Without it, every MCP call returned
RuntimeError: Task group is not initialized.

Also changed mount from /mcp to / (at end of route list) so the MCP
endpoint is accessible at /mcp rather than /mcp/mcp, matching the
sub-app's internal route structure.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/main.py

@@ -77,6 +77,13 @@ async def stats() -> dict:
     return s.model_dump(mode="json")
 
 
+# Initialize the MCP sub-app early so session_manager is available for lifespan.
+# streamable_http_app() creates a sub-app with a route at /mcp internally.
+# Mounted at "/" (last in the route list), FastAPI routes take priority and
+# requests to /mcp fall through to the sub-app — keeping the public URL at /mcp.
+_mcp_app = mcp.streamable_http_app()
+
+
 # ---------------------------------------------------------------------------
 # FastAPI app
 # ---------------------------------------------------------------------------
@@ -84,7 +91,8 @@ async def stats() -> dict:
 async def lifespan(app: FastAPI):
     logger.info("OpenBrain starting up")
     await db.get_pool()  # Warm the connection pool
-    yield
+    async with mcp.session_manager.run():
+        yield
     await db.close_pool()
     logger.info("OpenBrain shut down")
 
@@ -96,9 +104,6 @@ app = FastAPI(
     lifespan=lifespan,
 )
 
-# Mount MCP server at /mcp (HTTP streamable transport)
-app.mount("/mcp", mcp.streamable_http_app())
-
 
 # ---------------------------------------------------------------------------
 # REST endpoints (for direct API access and health checks)
@@ -126,3 +131,8 @@ async def api_recent(limit: int = 20, _: str = Depends(require_api_key)) -> list
 @app.get("/v1/stats", response_model=Stats)
 async def api_stats(_: str = Depends(require_api_key)) -> Stats:
     return await brain.stats()
+
+
+# Mount MCP sub-app at "/" last — FastAPI routes above take priority,
+# /mcp falls through to the sub-app's internal /mcp route.
+app.mount("/", _mcp_app)