Relevant quote: "In politics, a regime (also spelled régime) is a system of government that determines access to public office, and the extent of power held by officials. The two broad categories of regimes are democratic and autocratic."
It is true that as a term it has accrued some negative connotations due to the frequent use of the all-encompassing "regime" to speak of governments where their exact denomination tends to fall on the autocratic side of things. From a journalistic point of view, it is better to use a neutral term than a charged one; which unfortunately as you've noticed yourself it can taint the term to readers who are not familiar with its exact scope.
But it is correct to call it Biden's regime, just like the current administration (perhaps a better term given its popularity in the US) is part of Trump's regime.
With respect to culture wars and firing the "vaccine" hesitant it was a regime. Trump is now establishing a regime of a different kind. One can be unhappy with both.
I'm not the same person. But a vaccine which doesn't actually provide lasting immunity is a really shit vaccine. And while I wouldn't say that means it doesn't deserve to be called a vaccine at all, certainly many people think that.
No, it’s not. The tetanus vaccine saves lives and must be redone every so often. The cholera vaccine as well. There are many excellent vaccines that save lives that require boosters.