I have recorded video evidence! The battle goes like normal up until I summon Rogue One. Not only does it NOT reduce cooldowns on my ships but it does NOT reset the reinforcement cooldown on Profund...
Ideas
It's one of these 2 videos. They both show the problem of tenacity up getting dispelled and the one video shows cooldown reductions not applying from Rogue One. My next turn would not allow me to summon another reinforcement. Same with Outrider/ other allies not getting proper cooldowns when it's supposed to receive them. A combination of these issues happen every battle after the update.
https://drive.google.com/file/d/1xo4HH2mcXpYaK-LYC9d-zyMhRqxOxpQ1/view?usp=drive_link
https://drive.google.com/file/d/119qPTcXoTy7VbJleh-rCMHe5dqZA8W1j/view?usp=drive_link
Your Call Reinforcement issue is simple enough and not a bug. In your first video you can summon a reinforcement next turn. In your second video you can't.
The difference in the second video is Leviathan used Sabotage the Hangers between you calling Rogue One and Profundity getting another turn, which increased the Call Reinforcement cooldown back up to one.