Hi Sonia,
Do you have any BOOST_VERTICAL_INTENT query rules or baseScore applied in your Answers config? This could point to why the order of verticals is not changing. That’s because these two properties would rank verticals separately from the algorithm and would push verticals to the top all the time. Otherwise, the order should be set by the algorithm based on relevance of each vertical for the search query. If you’re currently using either of these configurations, I would suggest switching over to the new vertical ranking algorithm that came out with the Spring '22 Release Early Access. Particularly the bias property would allow you to weight a vertical more heavily but still rank it amongst other verticals.
As to the other part of your question, when a user chooses a vertical under the “More” dropdown, opening the dropdown will show the selected vertical underlined. It does not jump out to the navigation bar because the verticals are still in the original order set by the algorithm for that query.
However, I can see why it would be helpful to show the active vertical. You can submit this to the Ideas board for our Product Managers to consider!