It doesn’t appear to be possible to use Squarespace as an SSO client or server for Discourse. If you’re collecting money with Squarespace, it might be possible to use its API to add users on Discourse to a group to give/remove access, but that’s not immediately clear. Looking at the Zapier integration, it doesn’t look like Zapier knows how to handle anything but form submissions on Squarespace.
The only thing that it’s clear you can do with Squarespace and Discourse is embed Discourse discussions on a Squarespace page, which doesn’t seem like something you’re interested in.
I don’t think that there is any meaningful way to integrate Squarespace with Discourse beyond having the two sites link to each other and have similar color schemes.
Do you plan to use the Discourse subscriptions plugin for paid memberships or something else?