Hi there. Are you using the Enterprise plan on Squarespace and have access to their admin settings?
You cannot use Discourse as an OpenID Connect provider for Squarespace because it is locked to Okta. However, it is probably possible to use API/webhooks to sync paid users into the private group.
The only caveat here is that you will be locked into Discourse email code sign-ups, and profile changes cannot be synced like in open-source blogging alternatives.
Have you considered migrating from Squarespace to another platform, or is this something you don’t consider at the moment?