Anthropic profits from the PR, for one. And they likely hook these institutions on their products in the long term, for two – much like I was "stuck" on Azure until recently, thanks to their free startup credits pointing me to it a decade ago.
There are ways one can engage in financial engineering (is "accounting engineering" a term yet?) where despite not making a profit, you segregate a tax break, tax credit, charitable deduction, etc. into some other entity and then can sell that off as an asset that some other business that is making a profit buys and writes off against its own profits.