I'm not sure what exactly Doubleclick network is, but my proposal is - Google keeps Search + all Ads related stuff, including whatever doubleclick is.

What Google loses is everything client (user) side: Chrome, Android, Gmail and other personal cloud services. Lets call it Foogle :)

Foogle can charge Samsung et al. for its Android and personal cloud services it is running. And use it in its own Pixel devices too. And may elect to make it hard for Google to sniff it, like droppung doobleclick cookies in Foogle Chrome, provide "Foogle Private Relay", et cetera.