He also has an ongoing legal battle with PSG over his wages. I don't think it affects his performance on the field for Madrid though, whether they are playing in the Champions League or not. I took a quick look at his stats and it seems like the number is more or less the same over the least 3-4 seasons, so I'm not sure if his form is getting worse or we're over-scrutinizing him because he made a big move to Madrid. Granted he moves to a different league with different opponents, so it's hard to conclude anything from the numbers. I'm pretty sure he wants to win the UCL though, whether that hinders his goalscoring ability or not is unknown for now.
Mbappe was not happy in PSG recent seasons and PSG gave him good offers and promises, together with contracts, to keep him in their club season by season. At the end, their working relationship broke and Mbappe moved to Real Madrid as a free agent while PSG got no money from a transfer of one of brightest and most valuable super star players. They had many reasons to feel disappointed about it but about a contract between Mbappe and PSG, only their lawyers have enough information to say what party is wrong and will fail in the court.
So far, it seems that the court tends to recommend Mbappe to find an agreement with PSG, and it's an signal that Mbappe can not win this lawsuit if he continues.