How stop Microsoft Edge from taking over Safari searches?

Despite the implications of its title, please read Removing "Search Marquis" / "Search Baron" / etc on your own - Apple Community.

These "browser redirect" problems typically share a common cause. If you need help solving the problem please post those three screenshots. All three.

Please remove the "Intego" product in accordance with its instructions. It's utterly worthless; an example of junk that should never be installed on any Mac.

Confirm its complete eradication, and then please post three brand new screenshots of those same folders.

The decision is yours of course, but I believe you have allowed yourself to become misled. That's understandable because there are entrenched, multi-billion dollar moneyed interests in promoting fear and fomenting discord so that the enormous customer base of Mac users can be deceived into drawing that same conclusion.

Meanwhile, there are no lobbyists agitators or influencers who will say don't buy this or that product, or don't install something, like I just did. There is nothing in it for them. No compensation, no reward, nothing. It's a rigged system.

In the particular case of "Intego" yes I have used that product and quantitatively evaluated its performance. It's among the worst in a vast field of utter garbage. Do you really think some trade publication or "news" outlet is going to tell you that?

Removing non-Apple "anti-virus" junk is the first step in fixing a misbehaving Mac. Often, it's the only step. When presented with an ailing Mac, I won't even begin to think about what's wrong until it's been removed.