Is a buffer tank useful in a heat pump?

The Geisha, for example, is available up to 5kW, whereas the 7kW model can modulate down just as far. It doesn’t cost a fortune either, but you still need someone to connect it.

Of course, you need a few cycles a day, but that's no problem if you use the 17k to buffer.

24 like the OP? Otherwise, the consumption figures are absolutely fine.

But as I said, first get to the control system.

Nope. Unfortunately, first you have to decide whether to get a new compressor for €5k (the old one has already failed after 7 years due to the starts) or a new (more suitable) heat pump. And if you decide to repair, there's still the question of whether you can adjust the control system differently/better or have to accept that you will have to set aside €100 a month alongside heating costs for the new compressor in 2030.

For example, the Geisha is available up to 5kW, although the 7kW model can modulate down just as far. It doesn't cost a fortune either, but you still need someone to connect it.

Yes, but it is an air-to-water heat pump. I've installed two myself – anyone with basic skills can connect it. However, it is installed outside and not in the house. So that's even more effort.
But the OP already has a borehole for a ground source heat pump. It would be a pity not to use this huge advantage.

right, I missed that in the heat of the moment

Honestly? Install a heat pump that matches the house.

Your basic situation is that you drive a worn-out car with a residual value of €6,000. The engine breaks down and instead of buying a brand-new car for €9,000, you put a new engine into the old car, which also guzzles fuel without end.
Spend €200 on a proper heating load calculation and have a new heat pump installed – the brand basically doesn't matter. Even if the initial investment is more expensive. Heat pumps of this size should cost between €6,000 and 9,000 for material + installation (but more than uninstalling, putting aside, reinstalling, and bolting down is not necessary).

Thanks again for the answer!

Unfortunately, the heating is currently broken and a new heat pump probably won't be available and installed that quickly. How are we supposed to shower in the meantime?

What puzzles me is that with the neighbors, the identical heat pump at the same time in a similar house cycles 5 times less (12,000 vs. 60,000 starts). I hope that the technicians find an error on Monday during the compressor replacement at one of the points I mentioned (check dirt trap in the heating circuit / brine circuit, temperature sensor, bypass valve) and then the heat pump works like the neighbors'.

(Unfortunately, I can't decide whether to replace the compressor only after these checks.)

If you decide to repair, the question remains whether the control can be adjusted differently/better or if you have to live with putting aside 100€ per month alongside heating costs for a new compressor in 2030.

If no error is found in the mentioned points (check dirt trap heating circuit/brine circuit, temperature sensor, bypass valve) and no optimized control is possible (night setback, high hysteresis, possibly optimize block times or speed control so that lower speeds are used, possibly speed limitation), then the hope would be that the buffer tank alleviates the situation. That would also be cheaper than a new heat pump.

Thank you again for the answer! Unfortunately, the heating is currently broken and a new heat pump will probably not be available and installable that quickly. How are we supposed to shower in the meantime? What makes me suspicious is that the neighbors' identical heat pump cycles 5 times less often in the same period for a similar house (12,000 vs. 60,000 starts). I hope that the technicians find a fault during the compressor replacement on Monday at one of the points I mentioned (check dirt trap heating circuit/ground circuit, temperature sensor, bypass valve) and that the heat pump then works like the neighbors'. (Unfortunately, I cannot decide whether the compressor should be replaced only after these checks.)

Then let's proceed step by step. Repair, adjust, check, if necessary, buffer tank.