If you ask me the chances of Real Madrid winning the same things they won last season even with the presence of Mbappe in the club, I may not be able to give you a direct answer because the starting of Real Madrid did not show us that that energy is there again unless they will find their feet and start the process of the record keeping. There is no doubt that Mbappe is a great asset but we are yet to see this materialize in Real Madrid his present club. I would really want them to win at least a trophy this season to justify Mbappe's decision to join the club.
To give an answer about whether they will be champions or not, of course it takes time, at least we have to see the first half of this season is finished. of course we will be able to conclude how far their best performance is in the title race this season. Two draws in the early matches of this season also had no impact because the season is still long. The depth of the Real Madrid squad is certainly stronger this season, only Bellingham has not been able to play due to injury, which has affected Real Madrid's performance.
I think in La Liga, of course Real Madrid is very favored to win the title again because of the many improvements made in the transfer market, one of which is their success in recruiting Mbappe.