Based on the way implementers at those companies have talked about it, I don't think that's the desired long-term state of affairs. One thing Adam Langley mentioned in
https://www.buzzsprout.com/1822302/11122508-passkeys-feat-ad... was that the BLE handshake identifies the cloud service to use because they need to support corporations using their own services for all of their devices. Hopefully there'll be enough demand for that to ensure it's fully implemented soon.