Short answer: It is by design.
Long answer: This is not an SSO (single sign-on) solution, but our Forums uses your Opera Account as an OAuth2 identity provider.
To give an analogy: If you used your Facebook account to log in into Spotify, you can click “Log out” on Spotify.com and it may appear you are logged out of Spotify. But, if you open Facebook in a different tab you’ll see that you are not logged out of Facebook. Next, if you click “Log in with Facebook” on Spotify.com again, you will be immediately logged in without entering any credentials.
This is the same mechanism that we use. Spotify and Facebook do not share a session just like Forums and Auth do not. Logging out of Forums does not terminate the session on the Opera Auth servers since they don’t share session or cookie information. There is no “central SSO login.” Logging in our out of Forums is a completely independent action from logging in or out of Opera Auth.