What he is in is called Administrative Segregation, and it is meaningfully different from Disciplinary Segregation even though the physical setup looks similar from the outside.
Disciplinary Segregation, the kind most people think of when they hear "the hole," is a punishment. It gets imposed on an inmate for a rule violation and comes with restrictions on phone calls, visits, and privileges. Administrative Segregation is a housing classification, not a punishment. It is used when there is a safety concern, either for the inmate or for others, and it can be requested by the inmate himself. The fact that he still has phone calls and visits confirms this. Those privileges are among the first things stripped in disciplinary segregation. Keeping them is a clear sign his placement is administrative.
For someone dealing with mental health challenges inside a general population unit, requesting protective custody or administrative segregation is sometimes the only rational move available. General population can be an impossible environment for someone who is struggling psychologically. The noise, the social dynamics, the unpredictability, it can make everything worse. Removing himself from that environment before something happens is not weakness. It is survival instinct working correctly.
The classification may carry a stigma inside the facility among other inmates, but from a record standpoint it does not carry the same weight as a disciplinary infraction. It will not hurt him the way a write-up would when he goes before a review board or parole hearing.
He is doing what he needs to do to stay safe. That matters more than what anyone calls it.