Trump, at least, seems to like Putin because he's an authoritarian. Trump wants the same kind of absolute power that he perceives Putin to have.

Many of the SV fascists (and yes, this seems like a fair appellation to me at this point) also have anti-democratic tendencies via Curtis Yarvin and other such loons.

As for Vance, one can also find anti-democratic trends of thought among conservative Catholics in the US, under the euphemism of 'postliberalism' and/or 'integralism':

https://edwardfeser.blogspot.com/2023/06/postliberalism-econ...

https://www.pbs.org/newshour/politics/what-is-postliberalism...

You have to get through pages and pages of this tedious stuff to find out what they actually want, but the general tendency is towards some kind of Catholic/Christian state.