I am one of this terrible Bayernfans... (actually since I was a little child and as I am 52 that was somewhen in the 70s)
Sane needed his time - not just because of his ACL. The Bayernfans are very critical about their offensive stars - we already have seen that with Robben. Really fully accepted you just get when you do a good defensive job, too - and sometimes there is a bigger applause with a tackle of an offensive player after running from front to back then with a brillant offensive action.
He was critisized a lot in his first year - even if his offensive contribution was not worse than that of Gnabry and Coman - but last year Lewy and Müller carried the others. But other players like e.g. Müller and Kimmich were talking in favor of him in public and to the media and I guess that they and others had a big impact on him off the pitch, too. Nagelsmann gave him a new role - he now is more of a no 8/10 next to Müller than a winger - that works fine especially with Alphonso Davies on the left wing. Since then he really thrives - and that very consistently. In the league it is 5 goals and 7 assists in 1148 minutes - in the CL 5 goals and 4 assists in 500 minutes.
I know that there is not so much respect for the Bundesliga - but actually I think it is a lot easier to get results in the CL than in the Bundesliga - atleast when Bayern can play with their key players. Atleast in the group stage individual skills often are enough and it is not hard work to break through - whereas in the Bundesliga you need to play smarter to break down the opponent.