This is caused by the notification (Echo) icons' hidden text (only used by screen readers). The shape that you see is where that short text ("Alerts (0)", "Notices (0)") would be.
The issue is caused by an unfortunate DOM design in the Echo extension, Vector has nothing to do with it.

The fix:
https://github.com/DemianX0/mediawiki-extensions-Echo/commit/888753f5442169a557a60e5b2ca959cc556144b5
https://github.com/DemianX0/mediawiki/commit/7f983f61f2ec26e2e99133a6b77c17aa8729896e

Fixing this also allows to use the standard browser focus outline on these buttons (also follows the shape of the text), removing the need for the hacky emulation of focus with the border, which results in the lighter focus outline compared to surrounding links.

It's also more easily fixed by overriding the #p-personal { text-align: right; … } rule back to left for the li elements.

In T261171#6409551, @matmarex wrote:

It's also more easily fixed by overriding the #p-personal { text-align: right; … } rule back to left for the li elements.

Yes, that's right. I didn't think this line would be forgotten:
https://gerrit.wikimedia.org/r/c/mediawiki/skins/Vector/+/585629/52/resources/skins.vector.styles/layout.less#95

In that case the immediate issue is not in Echo.

@Demian - I re-checked frwiki (also checking T264339) - the issue reported in this phab task is not present there. Has it been fixed with the fix in T264339? However, the issue is still present in betalabs.

Compare - in frwiki the cursor tip shows "Your homepage" when hovering over the username link, but in betalabs the cursor tip still displays "Your notices"

frwiki wmf.10	betalabs

This has been fixed by rSVEC4ff30a16a0f4: Convert personal menu to use flexbox alignment. (in October 2020).