I am very fond of Merriweather (which I recently saw on a list of over-used fonts, for those who believe that you should use a different obscure and, hopefully, hard to read font in every document). It pairs nicely with Merriweather Sans, Cascadia Code, and for math Libertinus Modern, though I do have to tweak ex-heights to match.
I don't really like serif fonts, but the two that immediately come to mind are Noto Serif and IBM Plex Serif. Both are open source. I know Noto Serif is variable, but not sure about IBM Plex.
Lots! Start with the Google Fonts browser. This link should take you directly to a variable + serif list, and from there you can drill down into sub-styles, focus more on those with more axis, more styles, etc.: https://fonts.google.com/?categoryFilters=Technology:%2FTech...