In that case I'd just keep in the fridge straightaway until it's time to feed. I'm always wary of keeping bm at room temp given our warm weather. Later on if you've warmed the milk and didnt get to feed or baby didnt finish, you can keep it back in the fridge and rewarm just once.
If I have the milk at room temp for 2.5 hours already, I wouldn’t keep it in the fridge after that 😅. If I plan to use it later, I’d pump and store it in the fridge immediately, then heat it up when needed
Maybe do a taste test.