My main theory is that his deep mix of pitches all tunnel extremely well, and the tunneling induces better-than-average weak contact that gets him out of jams. He's also at the top of the charts in not giving up pulled balls in the air--the tunneling helps with that--so even when he gets hit hard the ball dies at the 380ft mark in centerfield. Among regular starters, the only guy who has a lower percentage of pulled balls in the air is Max Fried. Then Javy Assad. Then Jacob Misiorowski. Not bad! Assad has had an excellent pulled-air percentage throughout his career, so it's not a fluke. He still gives up home runs and hard contact, but he avoids the most damaging category of hard contact.
The stats about doing better with runners on base suggest two possibilities. First, he pitches better out of the stretch than the windup. Some guys just do better out of the stretch. I even recall a few pitchers that started pitching out of the stretch even with the bases empty. Second, he pitches better when he has to pause a little more between pitches, as opposed to bases empty when his tempo is extremely fast and he kind of grips it and rips it. Maybe slowing down a bit helps him focus. Or maybe the slight distraction of the runner helps him not overthink the pitch.
Also, very speculative, but i'd be interested in exploring potential mental/physical crossover in high-leverage situations. Does he subconsciously focus more in high-leverage situations such that those pitches are faster, or move more, or have better spin, or tunnel better, or whatever? Maybe the team has that kind of granular data.
I do think we're at the point where maybe there really just is an actual physical explanation for the results. I think interviews with hitters would be needed to confirm the tunneling theory, and the team might have better data to test out different possibilities. Also very possible regression is coming soon. Also very possible it's sorcery!