'signup_source' parameter in URL

Yes, that makes sense.

When a user clicks the “login” button on Discourse, they will be redirected to the URL on your website that you have added to the discourse connect url setting on Discourse. That URL will have sso and sig query parameters.

If the user doesn’t yet have an account on your website, I’m assuming you are taking them through the website’s registration process. It might be possible to update the code on your website to check for those query params and add some metadata to the user record to indicate that the signup was initiated from Discourse if the params are present.