Any side effects when substituting bigger capacity battery in place of smaller capacity?
If the thicker 2032 battery does fit into 2025 coin place of your key fob, there is absolutely no side effects. Your keyfob will just last longer.

The rumors you heard are utter nonsense. If a battery has no load, it means it is in "shelf", storage mode, and in the shelf mode no "chemical reaction" happens other than the normal storage aging , as in any other battery, 2016, 2025, 2032, or else. ("chemistry slows down", if you wish).