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Time.timescale = 0 doesn't break the game, but it would affect it if you decide to add  something like ui navigation using the keyboard. The way the game currently is, the most it could "mess up" is that you press the jump button and unpause. Now the character jumps because even if timescale is 0, your character can still receive inputs

Ok didn't know it can still receive inputs didn't really even think of that to be honest I will fix that.