There are 17 million employees in the healthcare industry as a whole, but so far it's a handful of healthcare systems that have announced this firing policy, primarily (but not exclusively) in NY and California, and an even smaller subset has actually gone through with firing people. Of course, even 1% of 17 million healthcare workers is 170,000 people, and even if 95% are vaccinated, that's still 8,500 people to be fired. And 95% is optimistic.
As to the claim that only hundreds have been fired, I'm not sure where you are getting your data. One healthcare provider in NY fired 1400 people[1]. 87% of New York's hospital workers are vaccinated and 64% of New York's general population are vaccinated.
So if the providers in extremely blue areas are faced with firing 13% of their healthcare workers, I'm a little skeptical that only hundreds will be fired, or that this is even a workable plan. But who knows, I don't think anyone has the full count for the nation at the moment. If you didn't just make it up, then please do share your source. More facts and less speculation are needed when discussing this issue.
[1] https://www.axios.com/new-york-northwell-health-vaccine-mand...
As of Sep. 28, CBN could find only 843. And, oh, look, they linked to https://www.fiercehealthcare.com/hospitals/how-many-employee...
Kaiser Permanente and Northwell Health were the largest with 1-2% of their workforces, although Kaiser's are on "administrative leave".
AFAICT, there aren't. Very small numbers have left (permanently or temporarily) jobs for that reason, whether fired, quit, or suspended. On the order of hundreds out of ~17 million health care workers covered by mandates.
Lots of political opponents have pointed to mass firings as hypothetical future consequences of mandate policies, and then reacted as if these hypothetical future outcomes were present reality.