Words are used to communicate, and language is fluid and changes over time. Clearly, zero-day is being used and understood by many to mean simply "unpatched", and so that is a reasonable definition. If ever you're arguing that a significant proportion of people are using language incorrectly, you're probably on the wrong side of history.

I think a "zero day" threat model and terminology is from the point of view of the blue team type of people running the system, not the vendor.

From someone running a system, it doesn't matter if the vendor had 0 prior knowledge of the vuln or if they had made 25%, 50% or even 99% progress towards a patch. The point is there is still no patch available for the vulnerability and your only defense strategies are the same as if the vendor hadn't known at all, so it's still a 0day.

If the vendor has had zero days notice then nobody has had any time to patch, so my statement stands.