After fiddling more I realized that it sometimes works the way I want it to work (just click away and the panel bar hides itself again) and sometimes the panel bar sticks permanently.
I found that clicking away from the panel does, indeed, hide the panel bar again (good.) Hitting the hotkey a second time to close it, however, re-enables the view setting on the panel bar, permanently revealing it.
bookmark panel hotkey then click away works as intended
bookmark panel hotkey then bookmark panel hotkey a second time closes the bookmark panel while permanently revealing the panel bar
Not sure if this is intended or a bug now that I've discovered this behavior
@WildEnte Glad it works for you. The panel uses the 24×24px variant and the icons are all within 16×16px. So a canvas of 24px and a favicon size of 16px centered within that will bring you to webpanel specs, should you care for that.
Should this feature be implemented then consideration should be given to standardising the behaviour across all panels that provide search functionality; currently that is not the case, for example Bookmarks and History where former's initial focus is not Search field but latter's is.