How do prisons deal with different categories of the mentally ill, specifically regarding Charles Manson?

How prison officials deal with mentally ill prisoners or inmates depends upon the type of prison and the nature of the individual inmate's mental illness. Mental illness and, specifically, the "insanity defense" are very complicated issues and the court may never definitively resolve them. The main reason for this protracted uncertainty is the mental capacity of some individuals who commit violent crimes.
At the core of the insanity defense are the notions that an individual tried for a crime either does or does not understand the basic concept of right and wrong, or that the defendant, at the time of the act in question, was not in control of his or her faculties. In other words, defendants in criminal cases may or may not understand that the act for which they were arrested and tried are legally and/or morally wrong, or they may, as in the case of legitimate (if exceedingly rare) cases of schizophrenia be able to argue that they were not cognizant of the actions for which they are being tried. Defendants with histories of mental illness who are functional adults when properly medicated may argue that, at the time of the criminal activity, those medications were improperly administered or lacking completely.
All of this serves as an introduction to the issue of incarcerating prisoners with mental illness of varying degrees. In the case of the recently deceased Charles Manson, his attempts at using the insanity defense were rejected because his history as a career criminal left little doubt that he was fully aware of the impropriety of the crimes for which he was tried. That Charles Manson was truly disturbed, however, could be considered beyond dispute. His posturing as a sort of messiah who dispatched impressionable lost souls to perform heinous acts certainly skirted the boundaries of insanity. As with many other prisoners, however, his mental state was a peripheral issue because he was deemed cognizant of the nature of his activities. Many prisoners can be deemed sociopaths and psychopaths. That is different, however, from an inability to differentiate between right and wrong, and Manson, as stated, knew what he was doing. That said, once incarcerated for his role in the deaths of Sharon Tate and the others, he developed a consistent record as a rule-breaker in every facility in which he was housed.
Manson's history is a textbook case of how prison officials attempt to deal with the mentally ill. His record as a mischief-maker and frequent attempts at escaping (more like aborted plans to escape, given that the hacksaw blades he repeatedly attained were always discovered before they could be used) resulted in a regular rotation between mental health wards for violent criminals and regular prison populations, as when he was incarcerated at the California Medical Health Facility and later transferred to San Quentin State Prison.
When in prisons like San Quentin, he was housed in regular cells, but subjected to greater scrutiny (hence, the discovery of his contraband saw blades and drugs). When in facilities dedicated to the criminally insane, the routine was already established. Because many violent offenders are of diminished or altered mental capacity, though, the basic principles of incarceration are the same. Staff house the prisoner in a solitary cell (meaning, no cellmate, as opposed to solitary confinement) so that he cannot harm another prisoner or, conversely, be harmed by a vigilante-minded cellmate. (Jeffrey Dahmer, famed serial killer/cannibal, was murdered by a fellow inmate disgusted by the details of Dahmer's crimes.)
In general, prison officials make the best determination they can regarding the details of how mentally ill inmates are treated. Because most prisons are filled beyond capacity with inmates, there is only so much most wardens can do with respect to specific prisoners. When circumstances warrant, prisoners with mental illness may be subjected to solitary confinement, which can actually exacerbate underlying conditions, or be housed in special prison wings set aside for particularly violent inmates. Those prisoners who are not violent but who suffer from mental illness are too often left to fend for themselves. Some may succeed in being segregated from the rest of the prison population for their own safety, but this is difficult because of the vast number of prisoners who want such protection combined with the aforementioned limited number of beds in each facility.
https://wgntv.com/2015/04/29/inmate-who-killed-jeffrey-dahmer-reveals-why-he-murdered-the-serial-killer/

https://www.latimes.com/local/lanow/la-me-ln-charles-manson-prison-behavior-20170104-story.html

https://www.rollingstone.com/culture/culture-news/heart-of-darkness-a-charles-manson-timeline-59292/