Search engine icon
It would be convenient to put the selected search engine icon near the magnifier, or even instead of it. [i]"To nobody, except those who will take pleasure here" [/i] (Franz Schubert, 1797-1828)
Well, you can request this from the devs as you just did, but it's not clear when/if they implement it. If you want a solution right now you can install VivaldiHooks. This is a collection of modifications to the Vivaldi Browser, and one of these does exactly what you want – replaces the magnifier with the currently selected search engine. The modification is called "searchfield-current-engine-icon.js".