Here is a quick explanation of what
@riceman is talking about:
https://www.sportskeeda.com/f1/wingtip-vortices-in-formula-one-why-are-they-formed
There are also the trails from jet engines that are caused by the hot exhaust condensing in the colder air.
Then there are the shock waves you can see as a jet breaks the speed of sound. Although these are likely not in play here.
I believe hammer trails could be caused by a combination of these things. I also believe humidity and pressure heavily influence whether or not you see a hammer trail. I have witnessed a few hammer trails in different calibers/cartridges. One incident that stands out to me the most was while filming a farmer shooting at a doe on a depredation tag. I didn't record the conditions but it was t-shirt weather, at dark and it felt like higher humidity as the temp was cooling when the sun went below the horizon. We were sitting on 5 gallon buckets and the beans were chin high while sitting. The farmer was shooting the 92PH out of a 6.5CM. The doe walked out of the timber, through a short grass waterway (valley maybe 20' deep, 60 yards wide at the middle and tapered to a point on the uphill side. Timber on the downhill side.) and into the beans. The first shot was around 150 yards, basically level with the top of the beans. Actually his muzzle may have been in the bean leaves and the bullet would not have been far over the top of the beans all the way to the doe. The shot missed and the doe didn't move, only looked around. There was a heavy hammer trail. He shot again and again missed and again a heavy hammer trail. This time the doe ran maybe 80 yards and stopped. She was roughly 175 yards at this point but on the opposite side of the short grass waterway but still in the beans. The farmer shot twice more and there was no hammer trail at all on either of those shots. Yes he missed both times. Yes he blamed it on the Hammers, even though he had watched me shoot a 1/2 inch group with his rifle earlier that day with that load. He also shot that load a couple of time to see where impact was in relation to his ELDX he used. There was just a little over an inch difference in sight in impacts. But the farmer was shooting unsupported and when the first shot missed, he lost confidence.
The main point is I believe the first two shots, basically level with the top of the beans, had a slightly higher humidity and possibly pressure than the two shots across the valley. Yes it would be a very slight difference but two shots produced hammer trails and two did not. All in less than a minutes time. At the 500 yard range we shoot at, there are days when we see hammer trails and days we do not. I have not tracked these conditions for comparison.
The spiraling hammer trail has me intrigued the most. I have seen and filmed it a few times. It appears to me the vapor trail is heavier on one side over the other. I think this enhances the appearance that the bullet is spiraling (wobbling) through the air. If the bullet was that unstable and spiraling through the air, you'd see it on paper. Elongated holes instead of round. You'd also see it with groups opening up and inaccuracy. Yet holes through paper are round and accuracy is superb out to 500 yards for me. Also when watching this spiraling trail I don't think it's the same rate of twist as the bullet. Someone could probably work this out by figuring the distance and counting the number of spirals on these videos. I'd be curious if it's the same rate of twist as the barrel/bullet. Also it seems to me the spiral trail is more pronounced with a slight cross wind as opposed to almost no wind. Reference riceman's first video with a more even trail vs other videos of the more pronounced spiral trail.
Now, back to the jet engine condensing air due to temperature change. Does a solid copper bullet retain more heat than a lead core bullet during flight? Do any other solid copper bullets with bands produce a trail? If no, then I'd say it's mostly due to Riceman's explanation. The way the shock wave comes off a squared shoulder of other brands vs the way the shock wave comes off the rounded PDR shoulder. Then consider the rifling cut through these bands. A square shoulder band meeting a square cut of the rifling vs a rounded PDR shoulder meet the square cut of the rifling. (Yes I'm using the term "square" very loosely here because of the spiral of rifling but I don't have a better way of explaining without pictures, that I don't have time to work on.) This rounded surface meeting the a squared shoulder could be similar to Riceman's tip of an airplane wing explanation as well.
Either way, I think this phenomenon is on the edge of being produced and takes a combination of factor to produce it. Otherwise it would be more predictable. And none of this explains the spiraling trail.
Just my thoughts,
kneedeep