You know, I'm not a huge Billie Eilish fan, but when she performed the Christmas episode on SNL last year I fell in love with her Christmas renditions.
Also love Haley Reinhart's rendition of Santa Baby. Very jazzy and fun.
A Yuletide reinterpretation of the Slayer classic, Seasons in the Abyss. Featuring members of Haken, Protest the Hero and Dream Theater.
It's not quite what you asked for as it's not an entirely new song, they add plenty of flourishes to it and entirely new lyrics, plus it's just so silly and fun
My joke suggestion is Santa Tell Me by Ariana Grande. Mostly because it gives Santa very interesting Christmas themed powers of mind reading and divination.
But I really enjoyed Sia's Everyday is Christmas album which is now on regular rotation this season. They are all new Christmas songs and got some bangers.
Sorry I had to post the absolute best one. Even if you don't like Marvel, the song about Santa by an alien who only has third hand information on him is absolutely hilarious and wonderful.
California Holiday by Kadhja Bonet. It is a new song, not a re-recording or a remix. I also like how it doesn't mention any particular holiday. It can represent whatever winter holiday you celebrate. https://www.youtube.com/watch?v=-EmcDL8psC4
You may like a song I co-wrote in an old band as a joke a few years back. We didn't do anything with it really, but it eventually got played on local radio (once) which was quite nice.