So far we have seen two free transfers by Bayern Munich side which has been their only activity. Konrad Laimer and Raphaël Guerreiro have joined the team in this way. But I must say that these are both really good additions to the team to have a bigger squad depth. But this won't be the only action they take of course.
A right-back and of course a centre-forward seem to be urgent for them to transfer. They have been interested in Kyle Walker for right-back position for a while and they are waiting on the player's decision. He still has one more year left on his contract but we will see. For striker transfer you already know that their priority is Kane. Apart from that Julian Alvarez is also rumoured.
I think the first priority for Bayern Munich is not hiring a good forward and goalkeeper to have alternative for Neuer because he is getting old, as forward they are waiting for Tottenham and Harry Kane because they know the first and best forward they can target is is currently Kane however I think Bayern Munich got some alternative options for Kane.
Its not really bad performance from Sadio Mane last season with Bayern Munich during 25 games scored 7 goals and has 5 assists, exactly he was injured and absent for many games make him difficult on the top performance. Sadio Mane have huge pressure exactly arrived there for replacing Robert Lewandowski consistent become top scorer in Bundesliga. But not fair with comparison between Sadio Mane and Robert Lewandowski because Mane is not as real central forward and he most likely play as winger position.
I think Sadio Mane can back to the top perform next season if Tuchel put him on left winger side than push as center forward, Mane will create many assists like did with Liverpool and how his contribution make Firmino and Salah scoring many goals. Need change with Mane position and Bayern have to sign or find new center forward next season.
Yes, I agree with you that the injury factor has reduced Saido Mane's performance, statistically he is also not a pure striker with number 9 like Lewandowski. Despite his temperament and tension with his colleague Leroy Sane Tuchel knows very well what Mane's quality really is because he often faced him when he was still coaching Chelsea.
We can also see how the Munich transfer market is moving this time, who want a centre-forward, namely Hary Kane, this shows the fact that they have no problem with Mane but they don't have a pure striker like Lewandowski.
What Bayern Munich wants is to hire a good forward to have a player like Lewandowski they had for years he was always the finest and top scorer in Bundesliga while I think Sadio Mane can't have the performance Bayern Munich needs and they are even thinking about selling Mane to earn money and pay the money for Kane.