Did more searching down the rabbit hole without much luck.
I checked ps -u not_current_user -o pid,stat,command and all the processes are “S” = interruptible sleep, so I guess that means that nothing is sending something to wake them up… Checking ps -u current_user -o pid,stat,command has everything “S” as well except, of course for ps which is “R” = running.
Nonetheless, current_user is running as normal, but not_current_user is stopped. I expected to see a “T” = “stopped by job control signal” for one of the parent processes of not_current_user to formally stop the non-current login.