It is worth noting that this involvement of the military is not being decided by the President, but by the Secretary of Defense, which suggests that the Pentagon is, in a key issue of of national interest, overriding the President and Commander in Chief. The US Congress has not been consulted on the issue.
This decision to mobilise the Armed Forces in the vaccination campaign is taken in anticipation of a national emergency. Although no national emergency has been called, the presumption is that a national public health emergency will occur, using the WHO Level 6 Pandemic as a pretext and a justification.

what about the Posse Comitatus Act? well, considering treaties with WHO (and other international powers) can override our constitution and laws we should not be at all surprised.

The UN has in the past overridden our constitution and laws and continues to try to this day, so what is surprising about WHO doing it. Then again, another pandemic like the flu of 1918, I'd really want society to have a lot of people vaccinated--the flu of 1918 killed between 50 and 100 million people. Some people will see that as a good thing, lessening our use of the earth's resources.