I once read that Rodrygo's playing time in Madrid during the Club World Cup has nothing to do with his departure, as said by Xabi. But I also don't really know what is actually happening. There are indeed many rumors circulating about Rodrygo, I heard that Liverpool and Arsenal are even ready to buy him. Given the current situation, if Xabi does not have a good backup player, it will be very difficult to manage the players' physical condition and fitness for a very packed schedule. So I think Rodrygo should be another option as the season progresses.
You are right about confusing rumors surrounding Rodrygo future at Real Madrid. Even though Xabi Alonso first said Rodrygo limited playing time was not sign he would leave it now looks like Alonso prefers other players and Rodrygo role has shrunk. With strong rumors that Liverpool and Arsenal want to buy him especially after big new signings like Kylian Mbappé it look move is possible. You are right that Madrid needs deep squad to handle busy schedule and if Rodrygo leaves without good replacement it could be tough to keep players fit. Having player like Rodrygo even as backup would be really useful for rotating squad and keeping everyone in top shape.
At the moment, Real Madrid has enough strikers and wingers, so if Rodrygo stays at the club without changing clubs, he will not have a chance of getting a place in the regular XI. Real Madrid has played in the last three or four matches, but we have not seen Rodrygo in the XI and we have not seen him come on as a substitute. Sometimes you have to compromise and Rodrygo must make that compromise. If he does not decide to change clubs at the moment, he will not be seen in the regular XI, which will only reduce his demand in the transfer market. There is still time to make this important decision for himself and choose a new club.