nuc11 was abandoned back in 2021 because of this. This question has been asked many times since, noone cares about 11gen nucs anymore. The agreed upon reason seems to be: 'Intel has crappy Linux support' and/or 'Nucs use evil lspcons to get from dp to hdmi', They need native hdmi, then mabe, it'll work. There's a recently opened thread about the new 12gen asus p42 NUCs, maybe it works there. Seeing is believing. here:
Intel Alder Lake 2160p @ 23.976 Hz passthrough HD Audio dropouts (i7-1270p/N100) - Page 3 - Hardware - LibreELEC Forum
And finally: go use a raspi or some other toy, don't spend more than 100$, it's not worth the hassle.