No. Plain and simply, No.
The facility is the property of a private foundation. That the foundation receives contributions (taxpayer money) from either the federal or state governments does not magically make it a federal- or state-operated entity any more than unicorns and glitter make it subject to state preemption laws which, by the way, do not apply as of right now to state agencies, or to federal gun-free/gun-permissable facilities.
And because there is nothing in the Constitution, as decided by SCOTUS, that precludes private property owners from doing almost anything they want to about firearms, the decision to say "No Firearms/No Weapons Allowed" does not in the least infringe on your 2A rights.
The folks trying to make a connection between the MM and Waterside are conveniently forgetting that Waterside received all of its operating funds from the City of Norfolk, which paid those funds to a "corporation" that was created solely to accept City of Norfolk's taxpayer funds and then disburse them to a contracted management company who handled the actual operation of Waterside. The accountant who worked on Danbus' case did an excellent job of documenting both Waterside's funding sources and the creation of the various entities to operate the place as being solely the creatures of the City of Norfolk.
Anybody wanting to find the record and the identity of the accountant has but to contact the Clerk of the Norfolk General District Court.
stay safe.