I was just on HAL Zuiderdam (Mexico), April 2022, and NCL Dawn (Tampa to NYC), April 2022, and Emerald Princess (British Isles), May 2022. These are current updates on the steam/sauna facilities situation in these three ships.
The Zuiderdam is an old tub and it has a free male sauna that will hold about 4, maybe, 5 people. It was mostly unused but I had a couple of pleasant conversations on the 12 day cruise, I hope it improves since I am on it for 45 days in the South Pacific with lots of sea days in October/November. The sauna is a bit tricky to find, and it's out of the way and has a noisy outer door and one shower and some hooks.
The NCL Dawn has an amazing setup, one of the best ever: a very nice sauna and excellent steam Both are modern and clean. The only negative is when someone hold the steam door open too long, it sets off a very loud alarm that a crew member has to turn off. Sauna and steam are male only and free and are in an alcove off the male dressing area, there are three showers. They are quite private. Unfortunately during the 11-day cruise, they were very little used.
The Emerald Princess has a free male steam room and sauna. Both are spacious and are off the male changing room and have 3 showers. Again, they were barely used on the 12-day cruise, but there was some visitors.