"The amounts of electricity or gas taken up by a heat pump must be recorded separately. Peripheral consumers (electric heating rod; heat source pump, control) must also be taken into account. The amounts of heat delivered by a heat pump must also be recorded separately. In addition to external electricity and heat meters, which do not each have to be calibrated, energy balances that are already integrated in a heat pump are also permitted."
Just read the last sentence of your quote.
I don't know of any heat pump that is subsidized that does not have the corresponding integrated meters.
But clarify that again with your craftsman.
You only need an electric heating rod if the heat pump can no longer manage because it’s very, very cold or if the heat pump is broken; otherwise, with proper dimensioning, you can always do without it! And you should!