The bad news here is that if you intend to use it specifically on Xbox Series X|S or Xbox One, you can only do so in wired mode with the included detachable USB-C cable.
Currently, the 8BitDo Ultimate doesn't offer a wireless mode for Xbox consoles. A firmware update could theoretically change that but for now, this is strictly a wired affair on that platform.
8BitDo has used Microsoft's wireless protocol already, as seen with the 2.4GHz dongle in the stellar 8BitDo Arcade Stick, adding to the puzzling absence of wireless functionality on the Ultimate Xbox controller.
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