refactor: lazy-load GmailClient to decouple API startup

backend/api.py

@@ -10,8 +10,6 @@ from fastapi import FastAPI, HTTPException
 from fastapi.middleware.cors import CORSMiddleware
 from fastapi.responses import FileResponse, PlainTextResponse
 
-from backend.worker.gmail_client import GmailClient
-
 app = FastAPI(title="PDF Trainer API", version="1.0")
 
 # Allow Vite dev server
@@ -37,7 +35,8 @@ CREDENTIALS_JSON = Path(os.environ.get("GMAIL_CREDENTIALS_JSON", str(BACKEND_DIR
 TOKEN_JSON = Path(os.environ.get("GMAIL_TOKEN_JSON", str(BACKEND_DIR / "token.json")))
 
 
-def _gmail() -> GmailClient:
+def _gmail() ->GmailClient:
+    from backend.worker.gmail_client import GmailClient
     return GmailClient(CREDENTIALS_JSON, TOKEN_JSON)
 
 
@@ -210,4 +209,4 @@ async def notify_unknown(payload: Dict[str, Any]):
 
 @app.get("/", response_class=PlainTextResponse)
 def root():
-    return "PDF Trainer API. Use /health"
+    return "PDF Trainer API. Use /health"