The FBI had already requested all Google records pertaining to Stone's accounts on May 4, 2018[1]. The warrant for the search records wasn't issued until June 18, 2018[2]. The FBI were not randomly trolling search logs; they were already on to Stone.
1: https://www.courtlistener.com/recap/gov.uscourts.dcd.204569/...
2: https://www.documentcloud.org/documents/6879593-180820-Stone...
Google has a dedicated group that investigates government backed attacks, like Russian disinformation and hacking. I never worked on that team while at Google, but I worked on a similar team at another company.
Normally nothing in a warrant will bar you from conducting your own internal investigation in support of producing relevant records. Sometimes that investigation yields results that are relevant but not within the scope of the warrant (the order you cite is only for a single Google account, not all Stone accounts). One way the legal department can handle such a situation is exactly what I laid out in my comment.
1. https://www.forbes.com/sites/thomasbrewster/2019/12/11/googl... 2. https://blog.google/threat-analysis-group/