I suspect a very common problem I've had several times. When the plug between the charger and the battery gets a problem, the charger shows a green light like it's charged. But in fact, it's only disconnected. A wire can easily break where it solders onto the plug, but then still make some occasional contact.
So you plug in, red light comes on, charger is working. You walk away, and 5 min later the green light comes on. You come back in a few hours, green light is on, and you think you have a charge. In fact, you only charged for 5 min.
34v is definitely not charged. That's your problem. The charging wires could also be disconnected other places, inside the battery, or inside the charger. Or there could be some other reason the charger doesn't work now.
The bms is working as it should, trying to use it at 34v causes it to shut off as it should. Then when you unplug, that resets it turning it back on. But still not charged, it will only shut off again. You need it to charge to at least 42v, and possibly as high as 45.