Valid point. But if Congress has already passed legislation giving the executive such authority then 1905 would still apply.
This pdf document put out by Congressional Research deals with the Federal Executive authority starting on page 5.
State and Federal Authority to Mandate COVID-19 Vaccination April 2, 2021
Looks to me like there is some pretty broad authority already granted to the Executive by Congress.
I don't think the executive can mandate that everyone gets the shot, but it certainly looks like they can quarantine or limit people's ability to attend certain functions if they aren't vaccinated.
I'm not advocating a mandate. I'm just looking at the law and precedents. And I'm not a lawyer.