Pokémon Legends: Z-A uses a real-time battle system where each move has a cooldown period before it can be used again. Move cooldowns are based on the Pokémon's speed stat and cannot be shorter than 3 seconds.
Moves from the regular combat system that modify speed do not affect cooldown in LZA. Instead, moves such as Agility or Curse modify the speed that the Pokémon moves on the map when following your trainer or chasing a target to attack. Dondozo plus Tatsugiri giving a speed boost also increases movement speed.
The time it takes for a cooldown to expire depends on two factors: the initial value of the cooldown, and the amount that is decremented each frame. Since most cooldowns will not divide evenly by the decrement, the last frame that clears the cooldown will likely add a tiny bit of extra time that is not perceivable by the user.
This explanation uses data from Legends: Z-A 2.0.0. I am not aware of it changing from earlier versions.
