Open Id Connect SSO on cross platform sites
The OpenID Connect module is designed only to login your users when they use the login button(s).

The SSO module will propagate the logins to your Drupal sites, if you are using Drupal as authentication provider/clients.

If you are using a cross-platform setup, you will have to create your own auto-login propagation in a custom module. Depending on your authentication provider, you may (or not) be able to define post-login actions to use. Or you may yourself utilize post-login hooks of your Drupal site to trigger logins on the remaining sites.

Unfortunately, the solution you are asking for not only depends heavily on your authentication provider, but also is far out of the scope of Drupal Answers.