Actually Sadio Mane is not able to adapt his playstyle to Bayern Munich, another thing is if you consider last season then you could see that time the management of Munich failed to use Mane properly. So Sadio Mane's performance was very poor. This is why Bayern Munich have Sadio Mane in their squad next season.
Mbappe is unlikely to join Munich. Perhaps he will go with Madrid. Or he will go to a Premier League club. I haven't heard any rumors that Mbappe is interested in playing in the Bundesliga.
Harry Kane is the perfect choice to replace Lewandowski. Kane is an experienced player. Kane also has the ability to score a lot of goals. And more importantly Kane's fitness is very good. As Bayern Munich aim for next season's Champions League, they want to strengthen their squad by any means possible.
If I was the manager in Bayern Munich I would pay more attention and be more careful bout hieing Harry Kane and spending money on him because they hired Sadio Mane in the same situation and he failed to have a good performance in Bayern Munich while they were expecting to see him be a good replacement for Lewandowski.
Harry Kane is also a 30-year-old player and if he joins Bayern Munich and fails he will be an old and bad-performing player for Bayern Munich just like Sadio Mane and I'm sure Bayern Munich will feel regret of spending this huge amount of money on him.
Sadio Mane and Harry Kane cannot be thought of as the same. Sadio Mane was bought by Bayern Munich as a replacement for Lewa. Lewa was a scorer. He scored a lot of goals with Munich. But Sadio Mane was never a scorer. Mane scored 22 goals in a single season with Liverpool, in the 2018–19 season. Bayern Munich management made mistakes in player selection.
Harry Kane and Lewa play almost the same style. Kane is a regular scorer in the Tottenham squad. Hopefully he will be able to score more goals if he is with a strong and experienced squad like Munich. But first he has to adapt himself to Munich's gameplay. If he can't adapt to Munich's tactics, Kane won't be able to score too many goals.