[Repeating this here at the recommendation of Ulises in their response to my ticket. This took place on an Xbox One X.]
I attempted to download the update, which then stalled at roughly 7%. From that point forward, my entire console became progressively slower and less responsive over the course of several minutes until it became completely unresponsive to all user input, then grayed out the screen while remaining on. After waiting for nearly 30 minutes in the hopes it might recover with time, i decided to shut the console down, which required holding the power button.
I restarted the console after a 5 minute wait, which lead to a gray screen identical to the previous one for over 15 minutes before beginning the start-up sequence. Upon reaching the account sign-in prompt and dashboard, a notification stating the Sea of Thieves update had been stopped, but console performance remained very slow with 1-5 minute waits for nearly every user input to process.
I attempted dozens of troubleshooting options available through Xbox's support and many 3rd-party forums and made no progress. On a whim, i uninstalled SoT from my console, and it significantly reduced the performance issues, but not completely -It remains almost unusable. The only option left to me, that i'm aware of, is to factory reset my Xbox and cross my fingers, which i'd very much like to avoid.
I was having absolutely no issues or signs of issues with other games or console performance earlier in the day until starting this update... Even if you have no solutions to this issue, i very strongly advise evaluating the integrity and stability of the patch and its delivery from Xbox's end; It would be disastrous if it were damaging or bricking people's consoles.
[Update: Since initially filing this in ticket form, my Xbox is now unable to pass the green start-up loading screen, no matter how long i wait. A factory reset appears to be my only remaining option before i start addressing this as hardware failure.]
