Their FAQ says they use Public Domain Registry to actually buy the domains. They are a wholly owned subsidiary of The Endurance International Group, who is owned by Clearlake Capital, a PE firm! So while it may shield you a bit, if you're moving from namecheap just to avoid PE then that may not be the most obvious choice.

https://faq.nearlyfreespeech.net/q/difftos

https://publicdomainregistry.com/about-us/

https://en.wikipedia.org/wiki/Clearlake_Capital