The nonprofit invests the tax free donations into the for-profit. It gets to keep its equity just like any other investor and as long as that equity held by the non-profit, there's no taxable event. If the nonprofit sells its share - since it was closely involved in the creation and management of the for-profit as an active investment - it becomes a taxable event under the unrelated business income tax rules. Until that time, the only "profit making applications" like ChatGPT and the API are run by the for-profit, which - I repeat - pays its taxes.

I genuinely don't understand why people think they've skirted taxation except out of sheer ignorance of how non-profits actually work. A 501(c)(3) is not some magic Monopoly "get-out-of-tax-free" card and the IRS isn't stupid, there's a ton of rules for tax exemption. They'd have a much easier time with tax avoidance if they were an actual for profit corporation with billions of dollars because GAAP rules are a lot more forgiving than non-profit regulations.