Since the dc have started secondary, and we’ve a wider pool of teachers, I’ve noticed this a few times.
If I email a Mr Smith and sign off Jane Jones, most people will respond Dear Jane, and sign off Sam Smith, and after that you’re on first name terms. Or they’ll write Ms Jones and sign off Sam Smith retaining a degree of formality.
But I’ve noticed that some teachers will use my first name but sign off as Mr Smith. If they want to retain their professional persona, that’s fine (although in this day and age it’s slightly odd), but in that case I think they should also address me as Ms Jones. It’s especially weird when I’m old enough to be their mum.
It’s not even in front of the children. I’ve even spoken on the phone like this “Hi Jane, It’s Mr Smith from dc’s school….”
It’s only a minority of teachers tbf , but I’ve only encountered this with teachers.