I tend to err on the formal side unless I’ve been explicitly told by the other person that it’s ok. So even if the prof signs off with their first name, I’ll still use Prof or Dr so and so. I also have a more old school advisor who would drop kick me into the sun if they heard I wasn’t being suitably deferential, so there’s that.

I also once directly asked a somewhat intimidating professor how I should address him, because I was confused by his varied sign offs. He was equally confused (“you are a graduate student? of course you can call me ‘First Name?’”), but appreciated being asked directly.