You describe this as if Bayern Munich could take the initiative and decide what steps to take next. But that is not how this works. Musiala is the one who decides how these negotiations will go. It didn't go unnoticed that the best clubs in the world area already after him. He can play this season without any pressure whatsoever and while Bayern Munich would like him to sign a new contract tomorrow, there is no good reason for him to do that unless Bayern Munich offers him a package that he can't resist. But Musiala knows that he is in good shape and if he stays healthy for this season and he performs well, his market value will go through the roof even further.
If I were him, I would put all the negotiation rumors aside and concentrate on football. Bayern Munich is onto it, but there is nothing they can do to pressure him into signing anything too early.
I mean Bayern could have a big part of it without a doubt, they could offer him amounts that he can't refuse, more than any other team in Europe (they probably can't offer more than some Saudi club) so it is still having to do with them a lot. If Real offers him 40 million a year for example, not that Real Madrid needs Musiala, I am just giving an example, and Bayern Munich offers him "only" 20 million, then yeah he could leave. So Bayern Munich has a responsibility to keep offering him the best contract they can afford to offer, without that they are not going to get much.
There could be some other teams who will chase after him, but as long as Bayern offers a good amount, I do not see him doing anything that crazy, feels like it would be just fine. I understand that it is not going to be just that easy to handle, but it's doable. Bayern Munich makes so much money, paying a part of that to Musiala is something they can afford if they want to keep him.