Frankly, I haven't heard of any other ad service out there. I know Reddit and Facebook make advertisers post directly on their platform, but who else does this internet-wide?

The people that run websites decide to show adds by adding a piece of software provided by Google. The website receives money from advertisers and Google gets a cut. They have a similar thing for Ads for apps. What Google does is collect data and uses advanced algorithm that decides which ads go where and who sees them to maximise revenue and value to advertisers.

Facebook works differently because it collects data about users (using shady tactics) and shows ads on its own platform from advertisers that want ads solely on the social media.

There are a few minor players but Google snuffs them out if they get too big. See what happened with DoubleClick, AppNexus as examples. https://www.nytimes.com/2020/09/21/technology/google-doubleclick-antitrust-ads.html

This is a type of business that favors economies of scale. Not hard to do.

So, explain this to me, as if I was child: which exact part would you break off? It seems to be the "ads" part, so how would it integrate into the search? Can it even function?

BTW, "ads" is the only division they own that mints cash. It would mean that maps, mail, android, browser would just die due to a lack of funds.

Google ex-divisio would place ads with and display them from the divested newco just as Google's customers do today. Customers such as (checks notes) Facebook: https://mlexmarketinsight.com/news-hub/editors-picks/area-of-expertise/antitrust/google-acknowledges-it-foresaw-possibility-of-probe-of-jedi-blue-advertising-deal-with-facebook

The suit doesn't claim Google's other businesses are leveraging an illegal monopoly, but the part of Maps which does is their ad business.