It doesn't even make sense if you're Atlanta. All you need from Belichick is 3 years. Who cares about your front office? If your personnel guy is good (and they like Fontenot), then he's still going to be there in 3 years. GM, the money guy?
If the Falcons lose McKay, it's not like they can't hire anyone else for the position.
This is likely about something else.
Maybe they saw Patricia coaching the Eagles D over the weekend, and he was floated as Bill's DC. That could be it. Belichick is loyal to a fault.
In retrospect, Belichick's big mistake is not hashing things out with the Krafts. If it were me, and there were that much rancor between them in the offseason over various thing (deciding on assistant coaches, trading Mac Jones, pick JuJu over Jakobi, and who knows how many countless other things [topped off with the successor contract for Mayo]), Belichick should've simply told Kraft ABSOLUTELY NOT to all of it, and ended the relationship right there. He didn't because he knew the Patriots are in the middle of a rebuild, and that any other situation would probably be worse. He made a mistake by not doing that.
Last year, he could've gone to the Broncos, Chargers, Commanders, Bears, Panthers (before they made their huge Bryant Young error), or Arizona.