There are two strategies described in this paper. The cyclic adversary, and the pass adversary. You are correct that the pass adversary is super dumb. It is essentially exploiting a loophole in a version of the rules that Katago doesn't actually support. This is such a silly attack that IMO the paper would be a lot more compelling if they had just left it out.
That said, the cyclic adversary is a legitimate weakness in Katago, and I found it quite impressive.
What is "cyclic" about the adversarial strategy, exactly? Is it depending on a superko rule? That might potentially be interesting, and explanatory. Positions where superko matters are extremely rare in human games, so it might be hard to seed training data. It probably wouldn't come up in self-play, either.
No, it isn't related to superko. It has to do with Katago misidentifying the status of groups that are wrapped around an opposing group. I assume the name cyclic has to do with the fact that the groups look like circles. There are images in the paper, but it is a straight forward misread of the life and death status of groups that are unambiguously dead regardless of rule set.
That said, the cyclic adversary is a legitimate weakness in Katago, and I found it quite impressive.