Problem:
The tooltip itself has a z-index of 801. The .admin-toolbar::after element which is part of admin-toolbar, has a z-index of 501. The #menu-footer has a z-index of -1, which is overriding the 801 z-index of the tooltip.
Changing the z-index of #menu-footer to a higher value caused the element to overlap .admin-toolbar and make the border disappear.
Tried applying a border-inline-end to the #menu-footer, which caused a flicker when the menu expanded.
The arrangement of all the associated elements needs be refactored to fix this correctly. However, a simpler fix is to change the hardcoded offset position of the tooltip in tooltip.js. Shifted the offset from 6px to 18 px.
Thanks @javi-er for assistance with this issue.
I am with @dalin at DrupalCon Portland 2024, and I am going to look at fixing this issue within the next hour.