I am setting up the outbrain server-side tracking using Stape Template. And the issue is that the click_id isn’t set in the cookie by the script. I don’t know the exact reason for it, but it’s just a fact.
You can check the 1 minute video on Loom I created
It’s impossible to set 1st party cookies from a tagging server that uses a 3rd party domain.
This is the reason why Outbrain tag does not work for you. To make it work, you need to use a custom domain for sGTM.