alt Hacker NewsHe has 30 kW solar so the registration with the grid operator already happened.
This isn't a grid limitation but a rule about safe home installations. The limits are low for things the general public gets to plug in on their own. Those simple limits don't apply to the same battery installed by a professional. Professionals would instead follow a more complex set of rules and make some calculations, allowing for much higher currents if done in the right way.
What you say is correct. Except: As the AC battery was installed four years after the PV system, I did have to register it separately with the grid operator, which included creating a new entry in the Martstammdatenregister. In other words, registering the PV system and the battery were two completely separate processes for me.