I don't think it is a wise decision for Bayern Munich to fire Nagelsmann at this moment. Because although Bayern Munich's performance in the Bundesliga is somewhat erratic, the team has been able to perform very well in the Champions League. And in the next match, they are going to face the mighty Manchester City. And I think the change of coach at the moment will have a bad effect on the players of the team. I don't think Munich can win against Manchester City.
I am also very surprised by this dismissal because it can be said that Bayern's performance is not bad, they can still compete strictly in all leagues. What I really doubt is that the squad that Nagelsmann has built will be defended by Tuchel, but that has already happened and we can only give Tuchel a chance to rebuild the Bayern squad. tuchel's first match as coach of bayern is against dortmund, that is an important match because if you win then bayern can return to the top.
Before they decided to sack Nagelsmann I'm sure they had considered what happened to Bayern Munich, including losing their playing style because they were handled by a new coach where there would definitely be differences from his coaching style, one of the forms of play. However, his dismissal was said to be very hasty, especially with the appearance of Bayern Munich, which can still compete very tightly as you said.
This is a new chapter for Bayern Munich this season, I just hope they don't decline with their new coach.
Talking about Bayrrn style of play, It is not going to be different. the only thing I will commend is the individual improvement which in hand will promote the team's performance.
The players will want to show their best to the new coach so as to have first team shirts in his square. Tuchel is a German coach, he is a good coach and I'm sure bayern Munich's management have seen what they need in him else they wouldn't go for him.