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Description
I think the markup is out of date, which is why this is happening.
Each tab has 2 focusable elements; the list item and it's nested anchor.
For keyboard navigation the list item is wired up to be the tab
which get's aria-selected
and listens to key events.
A mouse user will click the tab, but because it has a nested anchor element, the anchor takes the users focus, which has no semantic meaning and does not respond to key events.
If you match SLDS markup this should go away