Make dropdown menu button act like one
It's kinda not obvious how to key clicked without pressed, so here's an instruction: click it once, and close popup menu, then press Space bar. The trick is to activate it from keyboard, instead of mouse. Tab navigation from search field is currently broken, but I'll follow up on that soon™.
Thanks to this button, I discovered what looks like a bug in QtControls Templates: with a mouse press, a button stays checked but unfocused (due to main window handing focus over to a popup), but with keyboard activation via Spacebar the button stays both checked and focused while the menu is opened, so it is highlighted with an accent color like this:
I verified it with GammaRay which was generous enough not to hang while inspecting QtQuick views of System Settings this time (: