I can try , but my crystal ball doesn’t reveal much.
Overall, it sounds either like too little heat in the buffer supply or a control problem with the fresh water charging pump.
Too little heat: If your read tennis station temperatures are correct, there should be a thermal short circuit causing too cool water to enter the fresh water. We can investigate this if we have an exact hydraulic diagram including the internal structure of the buffer tank. How is the buffer charged, exclusively via the wood gasifier? What kind of return flow lift does it have installed?
Control problem of the charging pump: I could imagine this more. When little hot water is tapped, it starts to charge the fresh water. Due to the very decent buffer temperature, the fresh water heats up well (above maximum temperature) and the charging pump switches off instead of continuing to charge with low volume flow and producing a constant temperature at the fresh water outlet. So basically an override overshoot of the control. Causes can be varied: too high minimum volume flow on the tapping side, defective sensors, defective charging pump, etc... You can find this out if you at least observe all temperatures and the pump speed or the pump volume flow during a shower process. Do you have a chance for that?