Finally, this selection behavior could have been changed since 2.8. There's no reason sync mode needs to move every related UV vertex by default.
Hereโs a video showing the difference between Blender 4.4 and 5.0:
No more issues with shared vertices or cutting after selecting a face. No more confusing switching between UV Sync and Unsync modes.
Basically, it works like the UV tools in other apps.