Madrid is one of the big teams of La Liga who has always been the strongest candidate in the UCL competition and that is the reason why management and coaches always maintain the quality of squad performance. As you say if Madrid always has a talented player and all of Ancelotti is careful in choosing a player who really has a big talent quality and is able to help Madrid appear better. The injured player is always a big problem, but for Madrid it is not a big problem because all the players owned by Madrid are always ready to replace the position of injured players and have a good contribution.
And related to the El Clasico match, I think Madrid will still win the match. Vinic and other key players are always ready to beat Barcelona.
It is clear that Ancelotti will find a player on the bench who can replace the injured one, but does Real have a player of Carvajal's level on their bench? This is a rhetorical question, there is no such player, but they will just have to learn to play without him because he is out due to injury for a whole year. El Clasico is always a special game, and this confrontation is always unpredictable, every season due to different circumstances one of the teams can be stronger and despite Real's losses, I am ready to say that Barcelona can beat Real.
Lucas Vazquez was the first name to come up as a replacement for Carvajal, he is a natural replacement for Carvajal and has been playing in that position so far. Losing Carvajal is not the same as losing any other player, apart from his status as a key player in the Real Madrid squad, he is a leader who always pushes his teammates to be better. Ancelotti can overcome the problem in the right-back position by utilizing the number of players he currently has, in addition, Real Madrid can use the winter transfer market (January 2025) to bring in new players.