Not sure it matters from a public policy standpoint, as long as everyone is counting them the same way.
It seems like a thin reed though to suggest the dramatic surge in "unvaccinated" Covid patients are in fact partially vaccinated or simply less than two weeks from their second shot.
There’s not a sudden surge in the “unvaccinated”. Only the unvaxxed however are routinely given the PCR test upon hospital entry. Also, the usual dramatic decline in winter flu this spring took place before the vast majority were fully “vaxxed”.