Current result:

When the user focuses on search input, they're trapped in the dialog and there's no way to tab outside of it.

Expected result:

After the "Create button" the user tabs to the magnifier icon, then to the field, and then they can tab to the next element without opening the search dialog.

When they are on the icon they can enter the search dialog with an enter, space or AT key. 

When they start typing, they will open the search dialog.