I've been noticing that for at least a few months now. From what I've seen, it happens only in Levi mirrors. I inflict Fear on the enemy ship, most of the time the ship just takes a turn as if there was nothing going on. It's especially annoying since the enemy isn't at all affected, but if the enemy Levi applies Fear on me my ships miss a turn each time (just to clarify, this was during the post-Dagger and pre-Scimitar RNG fest, I don't know if it still happens). Aside from that, the issue with the cooldown is also there. If I attack an enemy that's Feared, they still are able to use their special.