my guess is the power supply. the pan cam uses a bigger supply ( im guessing to power for rotation) and by plugging a bridge into it it then needs more power than is being supplied. I’ve read a few posts on here about it going back and forth.
here is one where the user reports that Wyze support stated you would need a bigger power supply then what the pan cam came with. this was for an update, but that might have something to do with the issues you are having.
do you have a V2 camera you could try it in? if it works in a V2 and it works you know its not the bridge.