The supplier has incorrect meter numbers in the system - what to do?

You can also try contacting your network operator. Google "Netzbetreiber suche" and for me the first result is ovag. Locally, the municipal utilities don't provide the service but a separate entity does. A few kilometers away it's Westnetz. They should know their stuff and be able to help better than the municipal utilities (actually).

First, it would be helpful to know what is installed in your case.

Classic: One meter for the heat pump, one for the household. Both come from the grid and have a meter main fuse. After the meter, it goes to the respective consumers. Advantage: You can read everything directly, i.e. "consumption 1 kWh" on the heat pump meter also means 1 kWh consumption of heat pump electricity. Accordingly, the whole reading setup is simple.

Cascade: The electricity first goes through the total meter and then both to the heat pump and the household meter. The total meter is fed from the grid and has a meter main fuse, the household meter is fed from the total meter and has no meter main fuse. Advantage: If you have photovoltaics, you can supply both the household (because it is directly connected) or the heat pump (then runs through the household meter as feed-in but not through the grid) with it. It is sometimes called "Power-to-heat," which is technically nonsense strictly speaking, but it allows you to use photovoltaic power for heating yourself without the expensive detour through the grid. However, only the household electricity can be read directly (household meter consumption) and the heat pump electricity must be calculated from (total meter minus household meter). The grid operator does this and reports the consumption to the electricity supplier.

Who can say? The electrician must have wired it that way and the grid operator must be present and seal it. So "classic or cascade" is not something you just switch overnight via web portal, but rather rewired and resealed.

What to do? I would simply write an email or a letter (!) pointing out that the meter numbers in the letter do not correspond to the installed meters and request correction within a deadline. Only if they do not explain or correct this plausibly would I escalate.

I would first see if there is a separate network operator. That’s how it is here with us. And then they are responsible for such things.

I am pretty sure that we have such a power-to-heat setup. The electrician explicitly told us that back then. I just didn’t know that it meant what you just explained. :D Does that also explain the “wrong” meter numbers / are those possibly those virtual meter numbers? Or should they still match what is on the meters?

Regarding the electricity tariff: So far, with every change, they only wanted the meter numbers that are on the meters. So why not just register somewhere and directly read off and provide the correct numbers from the cabinet?