Expose DB connection error in /health response for debugging

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

app/db.py

@@ -13,10 +13,10 @@ def _params() -> dict:
     }
 
 
-def check_db() -> bool:
+def check_db() -> tuple[bool, str]:
     try:
         conn = pymysql.connect(**_params())
         conn.close()
-        return True
-    except Exception:
-        return False
+        return True, "ok"
+    except Exception as e:
+        return False, str(e)