I had a similar issue and it is a huge headache for everyone I’d say! Makes you feel bad for contacting your breeder, I know, but what are you supposed to do? I wouldn’t feel bad for “hassling”, easier said than done yes, but you need your paperwork and to get all your microchip information sorted. Sooner the better too, in my case there was a microchip record error with the council’s systems, two pups were down with the same number. Luckily I paid my rego first - I felt very bad for the other pup’s owner though!
Dogs NSW or your vet will be able to help you out with tracking your number within the databases, verifying what your number is should that be in issue, and get you a change of ownership application.That may require a statutory declaration. I believe that’s what you would have signed when you purchased but given the amount of red tape involved with registration, it might be easier for everyone for you to just do it again yourself.
Once you have that sent away, your change of ownership papers will be sent to you and later your mains or limited papers. It can take quite a while for the latter.
Don’t stress, it’s annoying but it will get fixed.