Tab order after the picker closes in a new session goes back to the beginning

Testing #335602

On Windows

1. In the new sessions view, tab to Interactive.
2. Press space to open the hover.
3. Quickly press tab twice. The hover should close.
4. :bug: Focus is on Toggle Side Bar on the top-left.

This issue also occurs with the permission picker, though I have to tab a few more times to close that hover. The issue also occurs when opening and closing these pickers in an existing session.