Real Madrid went as far as the Semi final in the club world cup and by contrast that way above 3 matches. Round 16, Quarter finals and semi final that's a total of 6 matches they played in the competition. You were right when you said he started the game against Al Hilal and that was his only start in the competition the two other games in the group stage against Pachuca and Salzburg he came in as a substitute which is not that bad but after that I don't think I saw him again. Well he might not fit into the coaches plans.
Real Madrid's success is comparative. Meaning that they already have great players, so Rodrygo needs to realize that he is not fit into their plans and he is a great player and he needs to leave for a club that will give him some time. But at the same time, why would Real Madrid give him away for free? It's obvious that they will ask for a ton of money for him, and that's the real dilemma.
Because if they are not planning on using him, only a few teams in the entire world can afford him, and if they do not buy him, then he will be a bench player all year, making him worth less next summer, and they would have an expensive asset in their hands which would not make sense. I would say, either find a team now, or play him often all season long.