Circulation pump in Viessmann gas heating

Hello everyone,
I would like to save some electricity and replace the circulation pump of my Viessmann gas heating system.
Unfortunately, I don’t know which one should be replaced, as I have two pumps (a Grundfos UPS and a Biral).
One is connected to the heating system and pumps the warm water into the heating pipes. However, there is a branch from this and another pump that is connected to my hot water storage tank at the heating flow.
Should both of these pumps be replaced or only one? I hope I have explained it clearly.

Thank you very much for your tips.

...I would like to save some electricity and replace the circulation pump of my Viessmann gas heater.

The existing one might be hydraulically precisely suitable, and a replacement could become a money pit
According to the description, a funny setup. Please post a picture or hydraulic circuit diagram here.

Regards.

NB: If you know nothing, you should rather avoid making things worse by trying to improve them!

So here are a few photos to make it more understandable.

Can someone explain to me why there are two pumps installed in the heating system. I would like to take advantage of the subsidy currently available in [Hessen]. Thank you

Since no one is answering you, I will share my layman’s knowledge here.

To my knowledge, hot water is always preferably heated.
So if you draw hot water and cold water flows from the pipe into the hot water storage tank, your left* pump is activated and the circuit for hot water preparation starts. In the tank itself, the heating water is passed by coils next to the domestic water and heats it. No water exchange takes place.
When the hot water tank is back up to temperature, the left* pump stops and the right pump for the heating circuit starts.
That is why there will always be at least 2 pumps.

While the old pumps consume a lot of energy, the new low-energy pumps are by far more energy-efficient (Energy Class A). Most likely, the pump of the heating circuit will run most of the time, so this one should be prioritized for efficiency checks.

I can’t tell you anything about the replacement itself.

* I assume based on the picture that your hot water tank is on the left and therefore the pump for hot water is also on the left.

Correct, on the left in the picture is my hot water tank. Do I understand correctly that the pumps only run when water is needed? Or does the pump for the heating circuit always run?