presumably, but I was consulting recently at a company that had a Workspace and I felt that
1. Google seems to want to put me into that workspace whenever I go to chrome and login despite not being at the company anymore.
2. I saw some search results in normal gmail / google search and vice versa that made me suspect there could be data shared between the workspace searches and my non workspace searches. Which would make some sense because I, like many people, don't zealously make sure work searches are never done when logged in to my private account. Example of search results improved - searched privately chose stackoverflow down page, searched workspace some days later, stackoverflow answer first result (not scientific, maybe I improved my search second time to get the stackoverflow result I was looking for) I noticed it and thought, huh, probably they merge this stuff.
So what I mean is does this happen:
Search private - switch workplace account - private searches enrich relevance of results in workplace account search - search workplace - switch to private - workplace searches enrich relevance of results in private account - quit job, start new job without company account all searches in private, quit job - start job with company account - private search history enrich relevance of results in workplace account search.
So sure, presumably not, but I'm not sure that we should presume without also confirming.