refactor: use shared get_db dependency

app/api/auth.py

@@ -2,7 +2,7 @@
 
 from fastapi import APIRouter, Depends, HTTPException, status, Query
 from sqlalchemy.orm import Session
-from app.core.database import SessionLocal
+from app.core.deps import get_db
 from app.models.user import User
 from app.core.security import verify_password, create_access_token
 from pydantic import BaseModel, EmailStr
@@ -11,14 +11,6 @@ from datetime import timedelta
 router = APIRouter()
 
 
-def get_db():
-    db = SessionLocal()
-    try:
-        yield db
-    finally:
-        db.close()
-
-
 # 로그인 요청 스키마
 class LoginRequest(BaseModel):
     email: EmailStr
@@ -49,4 +41,4 @@ def check_email_availability(
     db: Session = Depends(get_db)
 ):
     user = db.query(User).filter(User.email == email).first()
-    return {"available": user is None}
+    return {"available": user is None}