Am I still bound by the contract if I don’t transfer the service to my new address?

As a general rule, you are responsible for paying for a subscription until the binding and/or notice period ends according to the agreement. This applies even if you move to a residence where the operator cannot deliver the service, unless you have agreed otherwise with the operator.

You can ask the operator if it is possible to shorten the binding period or reduce the cost in another way, for example by switching to a cheaper service during the remaining contract period or if you can transfer the service to someone else.