BT stopped transferring ownership of YouView boxes to its customers for those supplied after, I think, 19 December 2019. So yours is yours.
Swapping the box through EE TV isn’t applicable, as you don’t have an ongoing contract, but when TalkTalk were doing it for failed owned boxes, they, rather sneakily I thought, retained ownership of the replacement box.
Youtube video incorrect. Only need to remove 1 screw from back and 4 from base. Unplug connector to front panel . Remove 2 screws that go through main board to release bottom half of case and then 4 screws that retain hard drive can be backed of enough to release it without removing metal plate altogether. Refit new drive in reverse order.
Tip. Make sure front panel connector is pushed firmly in or you'll not be able to get box to boot to maintenance mode to initialize reset and new drive recognition process. As others have said £12 on amazon for new drive. Bargain fix.