If you're experiencing issues with Xbox Messages not loading in your mobile Xbox app, here's a workaround you may want to try.
Clean up your Messages history via your console or on the Xbox Live website (https://account.xbox.com/en-US/Social).
I realized I needed to remove a lot of super old outdated message threads (aka "chats") with players I don't even follow today. But I found no option to "Delete" several of them since there were no messages inside the threads. It turns out that Microsoft emptied out old message threads when they upgraded their Xbox Messages system. I remember getting a warning / notification about this a couple of months ago but I did not clean up my Messages history then. Well, it turns out that as part of that process, Microsoft still left the empty threads (aka "chats") behind, taking up unnecessary space, which I guess the Xbox mobile apps were not programmed to handle.
So on the console, I found the following cleanup process the most convenient, at least in my case:
1. Move old empty threads (aka "chats") you need to delete by clicking "Move to message requests" (since no Delete option is available)
2. Go to "Message requests"
3. Highlight each empty thread under "Message requests" and click X to "Clear chat"