Even if you split the search and ads divisions into two companies, what prevents them from entering into a partnership and keep doing whatever they do now?
If/when business was unavoidable between two offspring companies, at minimum, I would expect them to have to inform the FTC, justify how it was unavoidable, and make the details of the transaction public. If someone complained that it wasn't unavoidable, quite possibly there would be additional penalties leveled on each of the participants.
It's not like some Monty Python character waves a wand and declares "you're not n different companies", only to wander off and never exercise oversight. Mind you, I don't think there's enough political capital in the world to manage to break Google up, but if it did happen then the judgement will have the teeth to make sure they're actually broken.
The separate pieces would not be able to engage in business together that constituted a combination in restraint of trade, because that’s illegal whether or not they are breakuo siblings. Breakups turn what used to be sole company actions into combinations, which, in and of itself, adds legal complications.
(Also, as soon as the ownership diverges at all, which will happen almost immediately, between the siblings, a lot of things that are problematic for market effects would also be breaches of fiduciary duty on one side or the other.)
And all of this leaves out the explicit targeted constraints that would inevitably be part and parcel of any breakup order.
That said, AT&T/Bell was broken up in 1984. The "Baby Bells" had all merged back together into 3 different companies (AT&T, Verizon, Lumen) by 2000. So there would need to be better protections in any potential breakup of Google or any other company today