I inquire about the transit hotel at PP 4/F, Zone A, T2 by emailing the lounge:
Thank you for choosing Plaza Premium Lounge Terminal 2 Zone A.
Sorry for the inconvenience , we keep the room only until 22:30 and the last check in time also until 22:30.
If you’re looking for a place to rest, we invite you to stay at establishments that operate 24 hours, providing a comfortable lounge service at the Plaza Premium Lounge, Taiwan Terminal 1 Zone D. Both terminals are connected in the airside of the departure hall, just need 15-20 minutes by walking.
So no 24/7 for that transit hotel
I guess I'll stick with showers at the 24/7 PP in T1 as you mentioned and try to snooze in the PP lounge.