Hi!
I do have and had similiar issues. I’ve regularly played to the edge between strain and pain. Although once the pain starts I would recommend stopping immediately. As you say yourself - your hands are useful and you don’t want to break them.
Should you take longer rests? If my impression of you is correct then I would say yes - probably a little longer resting time between practice sessions. Maybe it’s just projection though, because I also overdid it a little bit. I don’t think anyone can tell you how much you should practice and how long your breaks should be. Be honest to yourself, don’t force yourself and take care of yourself. Those are the three guidelines I set my training practice time by. Although the be honest to yourself is more about skill level than hand strain.
What I personally also do after an especially excruciating training session is stretch my hand out after playing, shake it out and relax. I can’t say how much it really helps though. It’s just something I’m used to from sports training and there it helps to stretch afterwards.
A thread also about training and how long breaks/recovery time should be: On bass playing and powerlifting (but it’s all individual as already said)
P.S: I’ve played for hours until module 11. Starting with Module 12 I could barely hold out 15 minutes. As with every new fretting/new technique - it get’s better. Just don’t overdo it because you are used to longer practice time without breaks.