But I don't think it's just Apple's airpods either: Most of the newer bluetooth headphones work and connect almost instantly with my iPhone; I have some Bose QC35 that I can report the same speed of connection of the airpods -- maybe even a little faster. I suspect it's related to some extremely modern bluetooth version or feature-set that might be difficult to discern from the box, but I have not dug into it deeper.
This being said, my airpods sit on my desk next to my Jabra DECT headset: Bluetooth is only almost instant, but DECT is actually instant. I first saw them visiting a cell centre (inside-sales team) team in Seattle, and so I asked about them and learned "we wear this thing making cold calls sometimes every few minutes, all day long, and it doesn't suck" and that pitch sold it for me. I wish it traveled better, because if anything rings (phone, skype, teams, zoom, slack), I pick up the headset and it answers on the computer at the same time, and I'd love (somehow) to have that experience when everything is packed in my rucksack.
As stated the only time I had a problem was standing next to an extremely large diesel backup generator which was probably RFI related.
Couple of years later, Sony has updated them half a dozen or so times, and I rarely ever get skips or jumps now. I have them always set to emphasise quality over connection, and they have worked perfect. You can buy them new on the likes of Amazon for ~£120 now, which is a bargain.
Sony just(?) released the XM4 which have a slightly better form factor and better codecs, so I'm considering them next.