[Aitrui]

As far as I know there is no solution yet to read the eeprom of the radio over OBD.

Check what's is the coding of your unit with VCDS or any other tool, like this coding 020007010000000001, after that you have to open the unit, desolder the 24c256 eeprom, read out the content with a programmer, search for your coding (020007010000000001) in the data, correct the 02 value to 00 so it look like 000007010000000001. Resolder the eeprom, and you are done.

YOUR coding could be different, don't copy and paste this example, but the first byte of the coding should be the 02 in every US radio unit.