Well, good news!
On one of the computers that had the jumplist issue, I just restored a backup from January 2025. After finishing, I DON'T click "Check for Updates" and let Windows automatically search for and install pending updates. Normally, it only checks for updates once a day when the computer first boots up. I repeat: DO NOT click "Check for Updates" either before or after. Let Windows do everything automatically.
PD:
I then restored the January 2025 backup again, clicked the "Check for Updates" button, and it didn't fail. This proves it's not the button, but a March update.