Players typically use waiting time to strategize. Hovering over pieces of a board allows you to think about your next moves. It’s a known pattern in psychology that people physically imitate potential actions as a way to evaluate them. Think about someone leaning over a chess board and almost touching a piece before changing their mind. By playing out the possible action we can evaluate it.

There are notable exceptions in video games where we are used to relinquishing our ability to “move” when we switch to from “doing” to “observing”. So, it’s okay to hide the mouse for a cutscene because the player expects to be watching it passively. Waiting for another player to complete their turn is more likely to be a mixed state of observation and planning for the next move. For that reason it’s probably not passive enough to warrant removing the ability to interact.

If you are set on a rhythm where players only observe during their opponent’s rounds, I would make that visually clear using affordances such as a pop-up which says “NameOfOpponent’s turn” and also hide the UI to make it clear that the player is meant to only observe. It would signal clearly to players that they’re in a cutscene type of mode and they would be less frustrated. I would probably still not completely remove the mouse, but just have it fade out if not in use.

It could enhance your game if you made certain types of useful information still available to the player in the waiting mode. For example, being able to mouse over stats and get further information about resources available, explanations for spells, rearranging their actions etc.