Two or more SAML clients login/logout sync


I would like to advise on how to solve the problem that has arisen…
I have two Discourse forums, I decided to move them to a single SSO based on Keycloak. I set up two SAML clients in Keycloak (for each forum, as you can see in the screenshot), respectively, set up the forums themselves.
Everything works great, but there are two things that are extremely annoying:

  1. If I login into one forum and then open another, then on another I need to login again. It is very uncomfortable. Is it possible to somehow organize “transparent” authorization between all clients?
  2. Accordingly, exactly the same problem with the logout. If I logout from one forum, then on the second I remain logged in.

Clients settings:

Thank you in advance!