Ivan
I've replicated this and know why, but no good idea how to "fix" it in a general way.

The Woo form there is a bit of an a11y mess as everything seems to be done with JS.
When you click the country field, Woo places the browser focus on a normal <li>
and not the search input.
If you click the search input manually with the mouse, it all works as expected.
Seems like an a11y bug in WooCommerce.
I'll keep thinking if there's a way to catch these kinds of mistakes in a generall way.