OpenAI was a 501C3. This meant donors could give money to it and receive tax benefits. The advantage is in the unique way it can reduce the funders tax bill.

A donation is a no strings attached thing, so these donors basically funded a startup without getting any shares?

Donations are not entirely without strings. In theory (and usually in practice) a charity has to work towards its charitable goals; if you donate to the local animal shelter whose charitable goal is to look after dogs, they have to spend your donation on things like dog food and vet costs.

Charities have reasonably broad latitude though (a non-profit college can operate a football team and pay the coach $$$$$) and if you're nervous about donating you can always turn a lump sum donation into a 10%-per-year-for-10-years donation if you feel closer monitoring is needed.

Officially, yes, but the whole situation with Altman's firing and rehiring showed that the donors can exert quite a bit of control if their interests are threatened.

That wasn't the donors' doing at all, though. If anything it was an illustration of the powerlessness of the donors and the non-profit structure without the force of law backing it up.

Microsoft is the single largest donor by a wide margin, and they were absolutely pulling the strings in that incident.

Did they donate, or did they buy equity in the for-profit arm? I thought it was the latter, and that Azure credits were part of that deal?

Unless the donors were already owners.

Donors can't be owners. Nonprofits don't have shareholders.

no that is not the test for nonprofit status