I'm specifically looking for the Battery Model number, like "A1234", for the sake of finding the correct replacement part.
Apple has never sold Retina Macbook Pro batteries as replacement parts except to Apple Authorized Service Providers who install them.
Apple did not design that battery to be user-serviceable. They GLUE the battery in place. Some Apple Authorized Service Providers will not service batteries because the the dangerous chemicals required to defeat the glue cannot be legally stored or used in a retail setting due to all sorts of safety, fire, and occupational health codes.
Therefore any battery part number is a moot point. The operative part number should your (shudder) chose to do it yourself is the computer's A number:

Any third-party who claims to sell original Apple batteries for user installation struggles with the concept of "truth."
The other issue is that far too many after-market batteries for Apple notebooks have a horrible reputation for being total cr@p. Some have destroyed otherwise working computers. And some at-home installers have also destroyed their computer trying to change the battery.
If you wish your Macbook Pro to live long and prosper, I strongly recommend you go to this Apple page:
Mac Repair & Service - Apple Support
and use the estimator to determine yours still qualifies for Apple service and the approximate cost. Apple stores generally no longer change batteries in-store—solvent issues again— so, even if you take yours to a retail store, they have to send it to a centralized Apple service facility where the work can be safely done. If you do the mail-in/ship-in service option you save time on each end.