I always thought the sauna issue in the US was odd. I grew up with wood fired sauna every saturday & special events for bath. Everyone went; friends come over, family, etc. It was an event for socialization, card games, gossip and lasted a few hours steaming up, cooling and repeating then into the snow or the lake
As an adult, I do not use dry sauna at hotels or gyms (US). My current gym has a wet sauna which is nice. I usually will look at a dude like he is odd if he comes in with trunks on. I am suspect of anyone with more than a towel to sit on and a hand towel to wipe your face. Growing up only the people who were "sick" wore clothes to hide their sickness, LOL.
So, it was very weird for me to walk in a sauna and have guys in trunks, I am uncomfortable and leave. So, long story short, nude with a towel to sit on and a hand towel to wipe off at the most. Just the culture I was raised in.
I would not shave in a public one here, but do all the time in the family saunas. You get the best and closest shave.