edit: breakthrough: at the end of the service manual I found the Sony part number: A-1832-983-A
Googling for that, I found some for sale at ridiculous prices: $70, €85(!!), £73(!!!)...
Has anyone got this done via Sony? How much did they charge for it?
For info, I have searched for all the numbers on the below pictures, and also scanned the QR code (L1476W1706AA0205). No chance.
If anyone recognizes the logo on the battery, please let me know.