I guess additional code will not be enough, as the way to put the charge controller into shut-down according to datasheet is to float the Isense-pin (which is hard wired under the hood).
(I noticed that I might have messed up with some translations 
just replace all the suspect with assume. That was what I meant all the way 
)
I did now do some additional tests, including BSP 2.0.8 (I can now confirm that I was using 2.0.14).
I did also try the difference between esp_deep_sleep_start() and esp_deep_sleep(), which caused some higher current consumption some time ago (ESP32-C3 power consumption doesn’t match to the datasheet). In my case, this did not make any difference (there was also no difference if wake-up-time was not specified at all (by me)):
- BSP 2.0.14, esp_deep_sleep_start(): ~218 uA
- BSP 2.0.14, esp_deep_sleep(): ~217 uA
- BSP 2.0.8, esp_deep_sleep_start(): ~216 uA
- BSP 2.0.8, esp_deep_sleep(): ~216 uA
The measurements were done with a different DDM (vs. oscilloscope last time).