There don't seem to have been any studies looking for differences between the different forms. Many of the studies are with K1 - so the effect would be from MK4, because in humans K1 is converted to K2MK4. Most of the other studies have their 'methods' section behind paywalls, but there's one showing a significant effect with K2MK7.

I'm a noob at molecular biology, but the effect appears to be via the activation of osteocalcin (which is also activated by aerobic exercise) - and all the K2 variants seem do this (the only comparisons have been between 4 and 7). Comparing MK4 and MK7 supplements for how long they’re detectable in the blood, the MK7 is around longer — I suspect that that’s an artifact of how the molecules are packed into chylomicrons and then taken up as the outer ones are taken up by cells first, but like I said, I’m a noob.

If you're looking for search terms, try "menaquinone HOMA-IR". My intellectual curiosity isn't strong enough to pay $30+ to read each study, but you may have better luck (or be more motivated) than me. :-)

BTW, if you haven’t listened to Gerald Shulman’s interview with Peter Attia (Gerald Shulman, M.D., Ph.D.: A masterclass on insulin resistance — molecular mechanisms and clinical implications) I recommend it for anyone trying to figure IR out.