Sounds like Princeton should be offering a CPT course for credits during the summer like pretty much every other top-ranked university. Students would likely have to pay some amount of tuition for those credits, but that is not too bad in the context of a paid internship.

USCIS (the agency that adjudicates OPT cases) is likely massively overloaded with processing border asylum cases at the moment - and recent media reports suggest they have been roping in employees who would usually work other parts of the immigration system to work asylum cases.