8.6.1 bug on omnibus: "Could not connect to the CI server. Please check your settings and try again."

After an upgrade to 8.6, a first Gitlab CI test went fine, but later someone reported to me that on merge request view he's getting " Could not connect to the CI server. Please check your settings and try again.". I pushed a commit to see if this could trigger CI and it did, but reverting the commit left me with exactly the same problem.

Logs don't seem to be showing anything. How could I diagnose it? I'm getting the impression that this might be related to #14452 (closed), though increasing the amount of memory available didn't help.