How could Taiwan - a country the US doesn’t recognize - join NATO?
Countries can do what they want. There isn't some magic spell, that forces countries to do thing, just because of some semantic game about whether a country is recongized or not.
Taiwan could simply join NATO anyway, if they get approved.
But no, most of Europe isn't interested in spilling blood over Taiwan, just like it isn't interested in spilling blood over Ukraine.
I'm not sure this is true. What actually happened is that NATO countries realized expanding NATO is in their interest so they ignored the "north atlantic" part of the treaty. While I doubt taiwan will be invited any time soon it wouldn't surprise me at all if Japan or even South Korea is.
Taiwan is thousands of miles outside of it.