I think you're honestly wrong, in my opinion Real Madrid gives more importance to the Champions League, in fact the season in which Barcelona won (two years ago) they actually abandoned La Liga to focus on the Champions League. I don't know about Manchester City, but for Real Madrid the priority is the Champions League.
The Champions League is their league so even if they are not focused winning the champions league shouldn’t be much of a problem for them but they are not a team to lose focus especially not under Ancellotti who has won almost every trophy with them now. I don’t think Madrid will prioritize the Champions League over any other competition, they will want to win everything all, anything they can get their hands on.
Sometimes it’s difficult to predict what will happen but i don’t think Barca will have a chance in winning the La Liga this season with the differences in quality between their signings and that of Madrid but we never can tell.
You need to understand that they put all the competition they are in as a criteria but if they were to choose in what trophy to lose the rather chose LA Liga instead of the Champions League. We all know its the highest among the league and football fans are more interested the UCL trophy which is why Real Madrid have a lot of fans who love them because of the number of UCL trophy they have lifted. Their fans brag about the number of trophies of Real Madrid holding the highest in their trophy room.
If Real Madrid fail to show good performances in the Champions League they might tend to lose more fans. Now that Mbape has gone to Real Madrid it will be a whole new era for the team as he would priotise the Champions league more to LA Liga