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.
In the Real Madrid squad, Mbappe is not the only star, Vini role is also crucial there. If Real Madrid manage to win some titles this season including UCL, Mbappe and Vini will compete with each other to win the Ballon d'Or. Both must contribute more to the team in order to win the individual award.
Yamal is still very far from the Ballon d'Or, he still has a lot of time to win it, if he continues to play for Barcelona and is able to maintain his current performance, maybe he will dominate like Messi and Ronaldo.