Mbappe is an ambitious player and he will want to win maximum titles as he can, and surely both La Liga and Champions League are big titles. Winning both big titles will increase competitiveness for Mbappe to win Ballon d'Or next year. This personal award is one of targeted awards in Mbappe career and is one of main reasons he decided to leave PSG and join Real Madrid last summer transfer season.
Mbappé will do everything possible to win as many titles as possible, in fact let's make a guess, Mbappé wins everything, Liga, UCL, everything, but the Golden Ball will be given to Lamine Yamal, don't doubt that, FIFA, the corresponding entities of these awards will surely give it to him, that's how it is, now if Barcelona wins something, they will also give the Golden Ball to Yamal.
The Golden Ball was for me the first award that became corrupt, now that at least for me is an award that is not worth it.
Haha that reminds me of the past where Ronaldo and Messi were competing for the individual Ballon d'Or title and of course since then many people have started to distrust the selection of winners which is no longer transparent, but that is not important now because for Mbappe he can get the UCL title because it is the title he is waiting for.
On the other hand, Yamal is also great player for Barcelona, he is still young and has very high value in the market, but I only see both players between Yamal and Mbappe have their own advantages in playing quality and they are very different.