The state only has to show that the care is reasonably required for your meaningful health.
This isn't really comparable; it would be like the prison forcibly removing your teeth because you may get a serious tooth infection and they don't want to be liable for that.
Here, my county and the one adjacent have two Sheriffs who are twin brothers, and are vehemently anti mask, etc. (Actually, one has since lost his bid for re-election).
Their attitude to the jails under their control was to _refuse_ to allow inmates to mask, even in dorm holding cells, and to refuse to vaccinate any prisoner against COVID who was in custody.
Here's the OJP opinion for your reference. Specifically:
> ...court decisions show that prisoners often do not have the right to refuse treatment.
I'd suggest doing some actual research into the relevant case law, e.g. Washington v Harper, instead of just googling until you find something that can be misinterpreted to support your position. While prison administrators have wide leeway to force treatment they are still required to show that it's necessary, either for safety reasons or because the treatment was mandated as part of the sentence of the inmate.