What does he think of the music lesson?
my ds HATES their weekly music lesson, and he gets to play a trombone so it isn't exactly boring, just that music really isn't his thing.
That is not an excuse for being rude or badly behaved, but it might explain why he needs to play the clown in that particular lesson.
My ds is year 6 and there are one or two things this year where I have said that you need to sort this, because next year there is much less flexibility (in his case it was getting out of the house when I said he had to leave, he just wanted to find his library book, and fill in his reading record etc and he wouldn't listen to the 'you don't have time')
So, I think it is fine to let him know that he is now expected to take some more responsibility, and be more accountable. I would suggest you put some firm clear boundaries, eg no screens at the weekend, unless teacher tells me your behaviour has been good during week. Get the teacher to specifiy what she wants changed, so rather than ''he has been good'' it should be ''he has spoken politely to staff all week,'' or ''he has done as asked by staff this week''
Get him to come up with alternatives to being mouthy when he is feeling irritated, and get him to come up with suitable repercussions if he is.
I also find that acknowledging his feelings goes a long way, so saying that he doesn't like music, and he and the music teacher don't see eye to eye, and that is life, it happens, even in your favourite job, but you have to find ways of coping, and being rude isn't an option, gets them to take responsibility for the situation.