So yes, I actually did not think about the fact that you can obviously get out the user’s default search engine if you trigger a search and then read the URL. (which requires the activeTab permission, but as that is only granted on click on a browserAction or so, maybe actually rather the tabs permission, anyway.)
Also, maybe it helps a little to see, why I want to do so. Basically it’s just a little workaround/fallback, which IMHO justifies no extra permission in my use case: