Microsoft has been promising YouTube playback with HDR support on Xbox since 2017, and after years of waiting, it's finally arrived.
As Flat Panels HD discovered, Google has added HDR support for anyone accessing YouTube via their Xbox console. It uses Google's VP9-2 video codec rather than the more recent—and royalty-free AV1 format, but the main point is it works now.
Google confirmed as much through its support site, stating, "YouTube is available in 4K on Xbox One S, Xbox One X, Xbox Series S and Xbox Series X models. The maximum resolution for the original Xbox One console is 1080p. HDR playback is supported on Xbox One S, Xbox One X, Xbox Series S and Xbox Series X models."
No explanation has been offered as to why it took so long to get this working, especially seeing as how Xbox owners already enjoy HDR on Netflix and Prime Video streams. Nevertheless, if you have a HDR-capable display hooked up to your Xbox, then enabling HDR streams on YouTube simply requires updating to the latest YouTube app via the Xbox store. Search for "YouTube" to discover the app, download it, and start watching.