Heat pump is not compatible with a water-bearing fireplace

I understood that the old version flows in a closed loop and the new version ends up in the large open water.

No idea. We don’t have anything like that and haven’t needed it so far.

Previously, the wood stove was connected so that it only heated the lower part of the storage tank, and stratification possibly occurred. Now it is connected so that the entire tank is flowed through, allowing more heat to be transferred to the contents.

Maybe, I can't tell exactly. But it really doesn't make much difference!
Both variants transfer the heat into the storage. Of course, it is important that the correct control and circulation pumps are connected.

Oh yes, you could have really used such calculations before planning and installing the heating system.
And even now it would still help to understand the problem.
With a proper heating load calculation, the heating system would certainly have been planned much more sensibly (smaller).
You could also have easily avoided the water-based fireplace!
Then you would now have significantly lower electricity costs, a longer-living heat pump, and maybe a small fireplace for decorative purposes.

Then it might be minimally better after all.
Layering with warm at the bottom and cold at the top is physically impossible, however. Therefore, the variant will also result in the entire storage being warm.
This was explicitly intended by the manufacturer for high-temperature inputs like fireplaces or solar thermal systems.

With such an clueless heating technician, I would somehow also worry that the tank might be brought to a boil.
Is it ensured that this cannot happen?

Intense!

In summer or winter? In other words, did the energy come from the roof or the fireplace?