A few related symptoms likely with the same root cause. Setup a test course with a few labels in a row. It may overlap with MDL-78897 and might be worth tackling them together.

1) If you tab into the region so you can use the arrow keys to press up and down to highlight each item, but when you press space nothing happens. If you press enter it does work.

Compare thing to when you tab into the top level tabs which does the right thing: you can press the left and right arrow keys and either the space key or the enter key selects the menu item

2) If you press either enter (or space when it works) you scroll to the label but then you lose keyboard focus. It should retain the keyboard focus ring on the item you selected and you should be able to continue to arrow down and then select further items are you are only scrolling the page and not navigating away.

Compare this to the second level tabs in the admin page which is correct (or in theory any other example where the tabs are anchors and not links). In this case you can press left or right and then press space or enter to show that tab, and then retain focus and keep on selecting other items.