Surely they have never turned a profit and are a long way from being profitable. If so, what taxes, current or back, would they owe?

Income taxes are not the only tax non-profits are exempted from. Sales and property taxes are others, depending on jurisdiction, California being one such state. I am not familiar if OpenAI-NP has been exempted from these

https://www.fplglaw.com/insights/california-nonprofit-law-es...

The money they received was tax deductible for the people who “donated it”. They money should have been taxed as income for either the earner or OpenAI.

I'd be curious if people were actually writing off their OpenAI bills as donations. That would be a big number for the enterprise deals, if they qualify as a donation

Surely the money coming in would otherwise have been investments exchanged for stock, which are not taxed until gains are realized.