They've tested 9.03 games on as low as 3.00, and they work. They released a new update at least for ps5 a few days ago along with an update for tales of arise. Chances are you won't be able to update the game.
I must warn you that one of the patches, either for 9.04+ or 4.50+ for ps4/5 respectively fixed a bug with one of the quests, which is impossible to complete without the update.
I don't know if there's any way to bypass being on latest firmware to download game updates. There's a bug to get on psn to download your games, but a lot of it is trial and error. I don't know if it works for game updates though. Plus latest I think requires 9.50, which I don't know if the keys are a part of 4.00