Hammering someone who doesn't see a problem is the best way to make a problem. It's not about being passive. It's about identifying the problem, explaining the problem, and coming to a mutual solution if possible.
Or, in other words, treating humans like humans.
"It’s emotionally draining to keep faking success or status that’s not legitimate." I'm saying get this sort of thing out of your playbook entirely. Of course someone's going to think they're doing well if you tell them they are!
If there's nothing that can be done due to the lack of give and take from the employee then your only recourse is to get shot of them, whether through transferring them to some other dept where they'd be better suited or letting them go