Agree with some of this. Bayern are in a mess but players look beyond the immediate, Sane will be looking at that move as being possibly one where hs stay the majority of his career, 5 years at least.
Sane is a young player and possibly the future star of their national team. BM will want him and with 12 months of a contract left in the summer they will feel they can do a deal with City. Will BM be in the CL, looks unlikely but another unknown, if they are out then surely for just 1 year. Will he want to leave if the clubs agree the price - debatable - who knows.