Just the general category of workplace health measures is too broad and ill-defined to specify whether it is constitutional or not. Particularly when you start stuffing things like vaccine mandates -- something unprecedented for OSHA -- into the bucket of workplace safety -- which is what OSHA is about (not "health", but safety, and primarily safety from occupational accidents).
You would need to make a case that the measure ties reasonably to interstate commerce or some other enumerated power and that it does not include anything forbidden to the federal government. The above is the test you always apply to any law, as well as any attempt to "stretch" an application of existing law to a completely new use case.
Personally, I think trying to turn OSHA into a public health authority is a bit of a stretch, as historically this has been the job of states - the NIH issued guidelines but states were the ones who implemented stronger or weaker versions of these guidelines. This is why you have some states requiring masks, and others don't. Some states requiring vaccines and other's don't. So what we have here is a massive new Federalization done under the guise of OSHA, whereas the enabling OSHA legislation was not concerned with things like public health measures, but with workplace accidents.