Your definition of Core Services is pretty unique and it would have been useful to specify that up front instead of burying it halfway down. What most companies call Core Services are the team(s) responsible for the service layer across infrastructure that is not directly tied to product features but necessary for Operations and Security… like logging, authentication, etc. Core Services is basically the software engineering side of the Platform/infrastructure group…. In some models it’s taken over by SRE, in smaller companies it tends to be the sister team to SRE.
It’s true that there’s always some mushiness around the boundaries of Core Services as teams reuse microservices built by Product Engineering and try to dump maintenance responsibilities for them on Core. But I’ve never encountered the definition of Core Services you lay out here and I’ve spent my career running Core teams.