how long should each climbing session be?

It depends on your goals for climbing and why you are doing it in the first place. When I started climbing I went all in and had 4 hour sessions on average I believe. I was quite obsessed. But, I also had a goal, to get as good as I could in the shortest amount of time.

Could I have done that with less time per session, definitely. I went 3 or 4 times a week, 4 hours each time, I wasn't really giving myself enough time to rest and recover, and I did get injured a few times. Looking back I would have definitely taken it easier and went the approach of quality over quantity. At least I would have had a better ratio to resting vs climbing. I would probably have been there for 3 hours at most and just 3 times a week.

But that is me and my body and my physical level, and that is how I can answer the question for myself, but for you, are you new to climbing? How long have you been climbing for? Would you say that you are generally physically active and are in good shape? These and more questions would help answer your question, you know yourself, and the key is to listen to yourself and to your body. If you start to hurt or get injured, reduce your climbing time. If you are capable of doing 3-4 hours at a time, go for it. If not, go for 2 hours even. If you can only do 1 hour, then do 1 hour.