I think a national mask mandate would likely be unconstitutional on a federal level outside of obviously permissible cases--such as on federal property like VA hospitals and national parks. Commerce clause jurisprudence hasn't been very favorable to national mandates for the last three decades. Federal authorities can certainly recommend masks. The Fed can also condition money on the state adopting certain policies...this is why the legal drinking age is 21 in every state (federal highway funds are conditioned on it).
Conversely, I think a federal constitutional challenge to mask mandates is a fool's errand, aside from some narrow as-applied challenges.
Health and safety regulations have always been the province of the states (see, e.g., Tenth Amendment), and thus the permissibility of any mask requirement will likely come down to state law, which will necessarily depend on the idiosyncrasies of that particular state. What does its constitution say? Has the legislature given the executive substantial emergency powers for things like pandemics, and if so what are the limitations of it? If the executive has such emergency powers, has s/he used the correct processes for imposing mask requirements? It's very likely that you could have two identical mask requirements, enacted through identical means, but it would be legally impermissible in one state but legally permissible in another.
Your horizontal federalist government at work!