The Real Madrid team has been strong since Pati but this season Mbappe has become even stronger due to the addition of Mbappe to the Real Madrid team. And this season will always be top and i can say manchester city can take second place and real madrid is likely to take first place. There will be a huge fight in the points table.
Mbappe just had a 5 years contract with Real Madrid, and he hasn't featured in any of the Real Madrid matches(Champions League or Laliga). To that, We don't know how his performance with Real Madrid will look like "good or bad" but we just hope it will be a fantastic one that keeps Real Madrid more formidable as they already are to lift the Laliga and Champions League trophy once again in the upcoming season
With the performance he has and with playing conditions that are actually not much different between Madrid and PSG I don't think Mbappe will take too long to adapt and can even immediately klopp with the current squad especially Ancelotti's scheme is actually quite simple so this does not require much more adaptation. But we know that Ancelotti always does some conditions that are beyond our reasoning for scheme and player placement problems so it is possible that for Mbappe he also has a new role when he is in Madrid just like Ancelotti did to Jude.
Apart from all that I think Mbappe will be able to immediately get his first trophy in Madrid by looking at the schedule later when Madrid will face an important match against Atalanta at the start of the season it seems like the right time to make Mbappe more recognized and he must prepare quickly for that because after all by looking at the current conditions actually even though we don't know what the future will be like but optimism for Mbappe is still very bear.