Barcelona management looks like they were careless in making a decision regarding Xavi, because if we evaluate this decision with full consideration, it is very annoying. Not without reason, Barcelona management took Xavi comments too seriously, I think all coaches would do the same thing if they were in Xavi position. It is very likely that Xavi next successor will also react this condition in the course of his career, because it will not be easy to fulfill all the demands of club officials with financial limitations that have not yet fully recovered. The competition for the trophy next season will be even more competitive, because Madrid as the main competitor still looks quite strong, and will even get stronger.
Barcelona management must act actively in the transfer window, regardless of how to deal with the financial situation, the aim is so that they are not left behind in the race for the La Liga trophy. Mbappe is reportedly getting closer to joining Madrid, even though the season not's starts, we can imagine how far Barcelona will be left behind if they don't improve the depth of their squad. Another concern is the process of adapting players to the new manager strategy, lucky if this stage does not last long. So I think letting Xavi go is the same as taking a bigger risk, regardless of other reasons that we don't know.
However, Barcelona management has considered and accepted the risk of continuing to expel Xavi. It can also be seen that Xavi was very affected when he became coach of Barcelona. So this is a good opportunity for new team soon. As you said above, the new coach's intervention may not necessarily be accepted directly by the players at Barcelona, because this requires another adaptation process and not necessarily all the players will feel compatible with the new coach.
When Real Madrid gets a player like Mbappe, it is certain that Barcelona will have difficulty beating Real Madrid. The strength of Real Madrid has increased very much because we can see that Mbappe is a player with very good achievements and skills and is respected by many other strong teams. If Barcelona wants to add new players it will not necessarily have positive results, maybe this will be dangerous for Barcelona because it could disrupt their economy again, new players with good enough skills require quite large salaries.