So I talked to our developers and they said this is basically the behavior of the autocomplete library we’re using. Not really a bug, but not really intentional.
We could potentially remove focus from the field if you go to another tab, but that might reset the tab index and mess up the flow for people who do like to tab between fields (and the Identify page is designed to be used with keyboard shortcuts and tabs).
I’m going to consider this closed. If someone wants us to look into changing the way it currently behaves, please make a feature request so we can gauge community interest in it. Changing it might mess things up for an even larger group of people who are using it the way it’s currently working.
Also, if you find yourself using a lot of the same text over and over, I highly recommend using a text expander, it’s much more efficient than switching tabs.