The power user thing in most "omnibars" that's been around for a long time at this point is that if you prefix search queries with a question mark ? you get an explicit search behavior (with your default search provider) and for instance auto-complete doesn't show recent URLs anymore.

Firefox (and Edge; don't know about Chrome as I don't use it) still have the concept of "Search Keywords" that you can prefix searches with to get into search modes for against specific non-default search providers. For instance in the Firefox bar you can type @wikipedia and go directly to a Wikipedia Search mode.