On the first subject, you are demonstrating likely intent from the private prison company so I wouldn't call it fallacious. On the second point, There has always been pressure from public health organizations to vaccinate at least healthcare workers. What has changed recently is the push to get EG public transportation workers vaccinated specifically for COVID. I don't think there's widespread support for that after the way everything went down.
The thing I think you're missing is that I'm not making the point there is never any ill intent from the people involved. Rather, you have to show intent in each case for the slippery slope to apply. In the case of private prisons it's pretty obvious that the organizations involved would like everyone to be incarcerated because there's a pretty clear income stream they can derive from incarcerated persons.
The other thing about "excesses of policy frameworks" is that there will always be excesses no matter which side you err on. What matters is the specific situation and the specific excesses and whether they were intentional or not.
I think in discussion we have to stick to specifics or we risk painting each other with a really broad brush. If you were to engage on a case-by-case basis I would probably say yes or no to slippery slope being a fallacy. Suggesting at the top that I think all applications of slippery slope are fallacious is painting with a broad brush a statement I made about the specific situation.
To bring it back to the original argument(and to paraphrase), I believe that going from "A woman in Tacoma who has been spreading TB and has been refusing reasonable requests to get treatment and to quarantine is being imprisoned" to "public health wants to throw us in the health gulag whenever we're sick and we don't immediately quarantine" seems like a stretch, and there's no evidence of the latter from the former or from any expressed or implied opinions that I've heard. So yes you need more evidence for that slippery slope argument for it not to be fallacious.