RPi4 is not the master of all possible codecs and cannot standby, but it's the best-supported device we install on, supports all or enough of the codecs you actually need, and has low-enough power consumption that you can just leave it on all the time (even in current times). I can highly recommended a flirc case (no fans so completely silent) and flirc USB for handling remotes. It's my family daily-driver combination.
I stopped trying to figure out NUC chip names and numbers about a decade ago so can't be much help on that front, but Any recent NUC without LSPCON should be reasonable and just work too.
NB: Kodi has no official Android maintainer because nobody (sane) wants to own the entirety of Android support, but 95% of the team who run Kodi on Android (and many do) use an nVidia Shield, so when something breaks due to nVidia firmware updates (as nvidia provides updates, unlike many other Android devices) there are always people motivated to fix the problem.