The biggest (by quite a margin still) is the Novo Nordisk foundation, but it is not really a new one. And its setup is rather different compared to OpenAI.
My experience interacting with Novo Nordisk is that, in their case, this model has led to massive inefficiencies.
The non-profit aspect has led to lots of internal politics and rigged hires. They are much more inefficient than a classical pharma.
Smells like tax evasion, but what do i know. Isn't IKEAs founder one of the richest people in Swiss?
Novo Nordisk might return to a more realistic market cap once other GLP-1 agonists enter the market, e.g. Lilly's.