As an update, I was able to resolve the issue by re-installing the PS4 client and using the PS4 version to log in and remove the character from puppets’ bunker. Once the character was teleported to another location, I was able to use the PS5 client to log in again.

This issue only affected my main character. I was able to create another character and log in without any problems. I’m not sure what caused this issue, but I’m glad I was able to resolve it.