waffleslop is looking to create a sign-up process for their Discourse, allowing users to register on either their WordPress (WP) or Discourse page and automatically be added to a specific group.
simon suggests using the WP Discourse plugin to set up Single Sign On (SSO) between WP and Discourse. However, adding users to Discourse groups would require custom code or the use of a membership plugin on the WP site. Alternatively, simon recommends using the Discourse Patreon plugin or Memberful.
pfaffman provides a PHP code example that can be used to add users to Discourse groups using the WP Discourse plugin, but notes that implementing the get_group_list_for_current_user function is left up to the user. If assistance is needed, pfaffman offers consulting services.
You could accomplish this by using your WordPress site as the Single Sign On provider for your Discourse site. The WP Discourse plugin has an SSO Provider option that can be used to set this up.
The tricky part is getting users into Discourse groups. To do this with the WP Discourse plugin you will need to add some code to your WordPress site. There are code examples on this forum that we can point you to for adding users to groups, but you need some way of determining what Discourse groups your WordPress users should get added to. One way to accomplish this is to add a membership plugin to your WordPress site and then add users to Discourse groups based on their WordPress membership level.
To have users signup and get added to Discourse groups without you having to add any custom code, you could look at the Discourse Patreon plugin. Memberful is also a good option.