The change of coach has put Rodrygo future at Real Madrid in even more jeopardy, especially since Xabi Alonso and Real Madrid will not stand in his way if he receives a suitable offer. Xabi Alonso style of play at the Club World Cup should have been an opportunity for him to prove his worth to the new coach, but in reality, he struggled to contribute to the team.
Arsenal interest in him could change the current situation, especially as Arteta is keen to have Rodrygo in his squad to add ammunition on the wing. He has to make the right decision for his future, it seems Rodrygo has to follow in Martin Odegaard footsteps to get regular playing time to improve his skills, in a situation like this, staying at Real Madrid is not the best solution for him.
I don't think that Rodrygo not being featured in matches is not something that has to do with Xabi Alonso becoming the head coach, Rodrygo's decline in performance is what has kept him out of being featured in matches. Xabi Alonso is also a coach that is very selective and picky, if he doesn't see much quality in a player he finds it difficult to feature such a player.
Rodrygo was one of the players that once made the headlines in 2023/2024 Champions League season after which he made some good performances but all of a sudden he disappeared and hardly they talk about him in the squad again. He can really become better if he joins Arsenal where he can get more playing time to his worth. I don't know how serious Arsenal will be in their quest to sign Rodrygo because he has good skills that can light up the squad so Arsenal need to go for him as soon as possible.