I would say that the postulates of quantum mechanics were created independently of the Copenhagen interpretation but are heavily tied to it. The idea of the "measurement postulate" or Bohm rule is a key part of that interpretation.

To get Bohmian mechanics there is no collapse and you need an extra equation that it is not in the postulates. To get many worlds you need to remove the Born rule (if that makes even sense). To get objective-collapse you need an extra postulate too.

However all that said, Copenhagen is often considered as incomplete for not being clear on what a measurement device is.

I would say that the postulates of quantum mechanics were created independently of the Copenhagen interpretation but are heavily tied to it. The idea of the "measurement postulate" or Bohm rule is a key part of that interpretation.

Even if all current interpretations provide the same results, you need extra considerations. To get Bohmian mechanics there is no collapse and you need an extra equation that it is not in the postulates. To get many worlds you need to remove the Born rule (if that makes even sense). To get objective-collapse you need an extra postulate too.

However all that said, Copenhagen is often considered as incomplete for not being clear on what a measurement device is.