A GFCI will trip if there is a current mismatch between hot and neutral OR if there is a connection between neutral and ground.
First, make absolutely sure you didn’t swap the ground and neutral connections when you replaced the shore power plug. That would create exactly this issue but could be dangerous to use as it would be using the ground as a current carrying conductor.
If you have an ohm meter, check for continuity between the neutral and ground of your camper’s power cord (with it unplugged, obviously). A fairly common cause of this is a failed electric fridge element that contacts the neutral side to a grounded chassis. Unplug the fridge from its receptacle to eliminate that cause. Other things to look for as anywhere neutral and ground and come in contact like behind receptacles.
Also, a PD can be left plugged in 24/7. Ours has been plugged in when home since 2007 with no water loss and good battery lifespan.
The hockey puck adapter is likely not at fault. They are a bit overrated as being the cause of all things evil with electrical. I’ve used one for 13 years including running the air conditioning. Their main downside is any heat from poor connections is compounded since there are two connections very near each other.