It seems to me that the Champions League will always be a priority tournament for any team, because it is the most prestigious tournament and because there are quite high fees that will stimulate the team to win. Whoever their opponent is, I am sure that they will have the task of getting out of the group to the playoffs, this will already imply very decent bonus payments. Moreover, Bayern has always strived to win this tournament, I think they do not have a task below the semi-finals or the final, so this season they will try to win the Bundesliga and the Champions League, but it is hard to believe in the second task.
The choice is still there for the kompany but there is still a trophy that is indeed a target by kompany must meet in his first season in charge of Munich, I personally may see if the Bundesliga trophy will be the main target that at least the kompany which must get, because after all losing dominance in the league last season has made a tremendous surprise to the management and also the Munich fans, so it seems that in order to restore their status as the rulers of the Bundesliga of course Munich will try to focus to get the domestic league trophies whether it is the Bundesliga or the DFB pokal, but as @Jody.Drummer said, When the Munich squad is able to maximize in the two competitions, of course there is nothing wrong with staying on those two paths competition, but if it is felt that they are better prepared to face one competition, it is clear that Kompany will prefer to prioritize the domestic league this season even though the Champions League is the most prestigious trophy among the other trophies available. 
the biggest question is
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Can Vincent Kompany handle his Bayern Munich players the same way he did at Burnley and Anderlecht?
source: https://www.bavarianfootballworks.com/2024/8/30/24221770/can-vincent-kompany-handle-his-bayern-munich-players-trasnfers-burnley-and-anderlechtVincent Kompany just started out, and as big as Bayern Munich may be, everyone needs to understand it's a new manager, and all new managers need time at their respective clubs. He had a decent pre-season, signed a few players that they needed, and now it's all up to them how they want to go forward.
The UCL draw just arrived, and I think the matches Bayern are playing are not that hard. Yes, the primary focus might be on the league right now, but they will also have to do at least decent in the Champions League. And that is not hard for the team that Kompany has at his disposal, so I would expect them to give very good fights in the coming days.
Regards
Duje
If I want to be positive I can say Kompany can be better than this because he is getting more experienced and after getting more experienced we can expect to see better performance from this coach time after time but it was still too soon for him to start coaching a team like Bayern Munich because there is more superstar players there is fans there putting the coach under pressure to getting better result and if he fails in any game he will be under more pressure from the fans and media.