A sauna is a dry environment (5-10% humidity), except for the short time when they pour water on the sauna stones. What you describe is called a steam bath/vapor bath or Turkish bath/Hamam, the temperature is low (50°C / 122°F) and humidity is between 65% and 100%. With the low temperature and high humidity is no risk of burning your skin and that is why at some pools they have small steam baths you can use while wearing you swimsuit. But steam baths have benches out of stone or plastic that are easy to clean with high pressure because the constant high humidity would destroy the wood used in a sauna.
I see, thanks for the correction, then that one was a Turkish bath.
Though about temperature, nope, I remember it was higher than the 50 you indicate (yes, there was an indication of temperature), though indeed humidity was extremely high, and I can assure you it was in wood, and you were supposed to go inside with towel, and eventually getting naked inside was not forbidden.
Maybe it was badly made, thinking to make it as a Sauna.
Scandinavian friends told me clearly saunas up there used to be made of wood, and I remember a Scandinavian trainees party where they even built a small sauna (did not use it though) inside the party hall, and it was all in wood (Scandinavians have a culture of sauna).
I think you know better than me how it is supposed to be, I can only comment on what I saw, not if it was done correctly or not.