As for next season, I'd say nobody. I'm already tipping them to win the La Liga Competition back to back but the Champions League? That I cannot make such conclusions.
But then, Barcelona are the closet to challenging and winning the La Liga Competition next season. They have to make hard decisons such as selling important players so they can get funds to add up much younger players.
In terms of La Liga next season, there is no doubt that Real Madrid will win and retain the title. Barcelona is indeed a big club, but as you said, its current squad is not as optimal as before. Girona, last season was really good, but it seems like some of their top players were targeted and left the club.
Then Atletico Madrid and others, they are very inconsistent with their performance, so it is difficult to reach or take over Real Madrid's position.
For UCL, yes it will definitely be difficult. If they can make it to the semi-finals again, I'm sure they will become winners again. But before that, it would depend on whoever he was going to fight. If it suddenly turns out to be Man City again in Round 16, yes it will still be difficult. But here, Mbappe's arrival at Real Madrid, one of the reasons is to be in the UCL final and lift the UCL trophy. So, he will try his best to make it happen, together with the entire Real Madrid squad, which in fact has been that strong before.
In essence, all clubs are improving their performance. Their main goal is also in their respective leagues namely the UCL. So, next season will be even tighter. Moreover, there are several UCL newcomer clubs whose performance improvements last season were impressive. So, this will become quite significant and tight later.