I guarantee this is happening in every state in the US right now.
According to this aggregation of stats, it seems about 1% of hospital staff have been terminated or quit due to COVID-19 vaccination compliance: https://www.beckershospitalreview.com/workforce/vaccination-... The numbers seem to be lower in highly vaccinated states and higher in vaccine skeptic states, so for California the number is probably lower than 1%.
I'm not sure if those numbers favor or disfavor your point, but I was curious.
Several of the hospital reports included resignations and early retirements, and at least one reported only voluntary resignations and zero dismissals, yet the numbers seemed to align well. But I was mostly just eyeballing an overall estimate of 1%. And the 1% and 20% figures aren't even directly comparable as I assume all health care workers (latter group) are a different group than hospital staff (most of the former group). Still, they're sourced numbers, which is something. Numbers with citations can be vetted, just as you did, and they can help anchor the debate.
- Much more admin and nursing staff than medical doctors. At the hospital I was at (in an overall left leaning area), I’d estimate between 10 and 15 percent of staff left. In comparison, only a couple doctors left.
- Relatively few firings. There was a strong push by management to pressure people into quitting. And for those that did not, many were placed on indefinite unpaid administrative leave. The rumor in the facility was that management did so to avoid triggering the layoff provisions in the union contract as a loophole.
As for your second point -- how management chose to get rid of the non-compliant workers is much more to do with limiting liability and expenditures. If someone quits, its harder for them to claim unemployment (but not impossible, see constructive dismissal) so many businesses would try to find a way to have you quit rather than fire you.