Two decisive things have happened. Firstly, there is finally sun! That is the decisive point. The new 19 W Anker solar panel without a battery produces the finest little electrons! Lying flat on the table with sun through the window it delivers only 600 mA at 5 V, so just 3 watts, but with a little position optimisation (slanting down from the sewing machine to the window) it manages 1 A. And after 4 hours of charging the little phone was at 83%. The second was the realisation that it is more efficient to charge the phone directly at the panel instead of taking the detour via the battery. And when the phone is full or in use, the battery keeps charging.
What also shows is that one problem of the challenge is that in the current cold (-5 °C outside today during the day) there are few good places to charge. The phone charges quite well outside, the battery only very badly. That needs to be investigated more closely. I will take care of that, and of the very pleasing usage statistics, over the next few days.