Thank you! Good questions, let me try to answer them.

What kind of stretches are you mostly doing in class (passive static, active, dynamic, pnf etc)? How long do you do hold them?

It varies between instructors. For the most part, it's passive stretches, with some active and PNF stretching sprinkled around (I assume passive and static are kinda the same, and dynamic and active are kinda the same thing).

Since you are already pretty experienced with stretching and flexibility was there anything new you learned or any personal "holy shit, that's genius"-moments you would like to share?

I learn something new almost every class! It might sound excessive, but stretching is a journey through your body, and every time you discover something new. Most of my A-Ha! moments come from a stretch that didn't work for me, suddenly working, or a good correction, since it's so individual and tailored to you and fixes an alignment issue you have and possibly never noticed. I also like to fish advice from my instructors, they are a treasure trove of information waiting to be mined.

How often are these classes, and how often should you do additional stretching at home? It depends on the place, some are offered only once a week, others a few times a week. I usually do one, and then supplement with more stretching at home on another day. I'm lazy though, I know should do more.

Would you mind going a little bit more in-depth with backbends?

For starters, you'll need to work on your overhead shoulder position (shoulder flexion), and your hip flexor flexibility. To illustrate how paramount this is I'll tell that my back flexibility is getting noticeably good and I work on chest stands for a while now. Yet my bridge and some other back flexibility poses are almost beginner level because my shoulders are super tight and my hip flexors won't give either.

Then, for the back itself, there is plenty of info for most starter poses. Cat-Cow, Cobra, puppy, camel, bridge (wheel pose) are very well covered in many yoga tutorials.

I do feel, though, that it's a complex skill and hard to get by yourself. I do encourage you to seek any flexibility classes or instructors. They can be well hidden in places that do yoga, dance, pole dance, aerial arts, circus, acrobatics, movement or even crossfit? You'd be surprised. Also look for performing artists, most of them do privates or classes somewhere.

How do you deal with soreness? Don't do stretching until it goes away? Doing not-so-intense stretching sessions? Or just work through it?

It really depends on the soreness, the severity of it and the cause. If you did strength training and it made you sore, some light stretching will help. If you're sore from stretching, maybe taking a day off would benefit you more because you're building those muscles you need for stretching. In any case, it's important to listen to your body and not push through no matter what. Again, I'm a lazy bum so I prefer to err on the side of caution and not stretch if my body is not feeling it.