Now that the sun has been out for a few days and I can even keep the phone supplied with the small gizmo, I see that I am also sitting in front of the screen 25% more per day again. So it shows directly that with the prospect of being able to charge well again the next day, usage immediately goes up again.
The positive thing is that when charging at the panel, the phone has to go out on the balcony or in front of the window. That interrupts constant availability, and besides, the panel is now already giving 1.26 A when I charge the small battery with it.
That is an interesting point anyway, because in less than ideal lighting the phone charges poorly at the panel whenever the average power is below the target 5 W, since only the voltage regulator "buffers" a little there. With the small gizmo the big battery is there, so the charging current is always available as long as there is something left in it. The solar panel then charges the battery, which can be charged with any current. With the phone that doesn't work, because Apple interrupts the charging process on the phone side when the target charging current is not reached. As a result, charging starts as soon as the regulator has received enough current from the panel and conjured the required 5 V out of it. The phone then charges briefly, the regulator's buffer is empty, the current drops and charging is interrupted. Each time the screen switches on to show that it is charging or not, and in doing so more power is used than charged. Conclusion: in good sun it is ideal to charge the phone at the large panel outside; in overcast weather it is better to charge the battery with the solar gizmo and then the phone from the battery.