Update #2 [Thu 2nd Nov, 2023 03:00 GMT]:
Microsoft has provided another update to the same source, confirming connections via the USB and 3.5mm ports on the Xbox Adaptive Controller will not be impacted by this new policy. Third-party devices designed for accessibility should also continue to work through this device.
Update [Tue 31st Oct, 2023 0:05 GMT]:
A Microsoft spokesperson has issued an official response (via Windows Central), explaining how unauthorised accessories can "compromise the gaming experience" on Xbox consoles:
"Microsoft and other licensed Xbox hardware partners' accessories are designed and manufactured with quality standards for performance, security, and safety. Unauthorized accessories can compromise the gaming experience on Xbox consoles (Xbox One, Xbox Series X/S.) Players may receive a pop-up warning that their accessory is unauthorized. Eventually, the unauthorized accessory will be blocked from use to preserve the console gaming experience. For a full list of accessories that are supported on Xbox consoles, please visit www.xbox.com/accessories, our support pages here and here, and our Designed for Xbox Partner Hardware Program page here."
Since this announcement, various accessory manufacturers have been confirming the status of their own products beyond this update. It remains unclear if products like XIM or Cronus Zen will continue to work, but as a reminder, everything that's been "officially licensed" is in the all-clear.