Auth0 is the identity provider.
Multipass is a great option if it’s available, but as mentioned, it’s an enterprise solution, i.e. you need to have Shopify Plus. If you’re using Multipass and Auth0 (or another identity provider) this is relatively straightforward. As to integrating multipass directly with Discourse (i.e. the original question), you’d need to build a plugin, but it wouldn’t be too hard.
In @outofthebox’s case Multipass wasn’t available. I implemented it using a shopify theme, Auth0 Single Page App SDK Code Grant Flow with PKCE. - Auth0 Docs and a number of Auth0 rules. It’s somewhat involved. I hope to publish it at some point, but we’ll see.
There is probably scope for a Shopify Discourse App actually which would make this somewhat easier. I started to build it at one point, but found a more efficient way for the goal at hand.