I'm not sure when a company begins to not be a start up, but by the time they have a wave of news claiming their product kills teenagers, or they're engaging in antitrust, or they're effectively using space labor, that's when they are definitely no longer a start up.

That hasn't happened yet for OpenAI, but I'm sure it will happen eventually, and then we'll know.

I think you stop being a startup when there are engineers who do not know the CEO. I would guess OpenAI is still a startup by that definition (they don't have that many engineers IIRC) but I don't actually know.

That's really a function of what kind of CEO the company has, and what do you mean by "know". I worked remotely for a company employing hundreds of people, around for couple decades and with offices in different regions of the world, and I still got to talk to the CEO a couple times, and he knows me by name, all by virtue of bumping into him a couple times on corridor while on one of my infrequent visits to the office.