Add NC Unified Search to browser search engines

I wonder if there is a way (a URL) to add the unified search of nextcloud to my browser’s search engines (like google, bing, ecosia etc)

So that I can start searching directly from my browser’s address field (after a user-defined search shortcut)
All that is needed is a search URL, like
(%s will be replacedy by search keywords)

As a second step, showing results in the browser bar just like on the nextcloud web-interface.

Is there a way to do that?
It would save all the clicks of “open your nextcloud page (wait for load), click on top right search button, start typing”


Perhaps this could be accomplished by hosting searx and exposing your nextcloud to it via api.