For my phone, I use Graphene OS. What would be the best desktop Linux option to match the level of security and privacy that GOS provides?
Depends on what you mean for security/privacy. You can use Tails or whatever and have everything encrypted and then just be logging into your Facebook account on Chrome without an ad blocker.
Most Linux distros are secure enough for the average person who isn’t being targeted by some crazy state level actor. If you’re particularly concerned stick with a distro that has a security team like Debian. As for privacy that has more to do with the sites you browse and have accounts with but obviously avoid Google (I just use Firefox instead of Chrome) use an adblocker like ublock origin, along with maybe something like decentraleyes.