how do preserve focus of a text input while allowing hovering of buttons?

[MichaelBelousov]

I have a searchable dropdown widget that looks like this

I focus the text box on the first frame so users can type to search the list instantly

But then if they hover over a button or elsehow focus a separate widget before starting to type, the text input loses focus and they need to click on it to refocus.

I am guessing DVUI uses focus to e.g. tab-select through lists of buttons like mine. But in other contexts (e.g. some browser UX I am used to), you will not lose keyboard focus of the text input.

Is this a DVUI problem or is there a better way for me to do what I want?

[MichaelBelousov]

@david-vanderson pointed me to the suggestions widget in the demo! It looks like what I want, but I didn't show above that I actually use submenus which it doesn't seem to support. I'll go add an issue for that feature but I think this is mostly solved