As a (fully vaxxed) US citizen traveling in the EU with a flight out of Budapest to the US, can I fly into BUD from a Schengen country and transit out of BUD? Say Madrid to BUD then (on a Different ticket) BUD to Miami without leaving the airport?

I know we can't enter hungry as US citizens (by air at least), but hoping overnight transit via 2 different airlines is ok?

Alternatively, can I drive into Hungary from Serbia (US citizen) and then fly out of Budapest?