When running on battery power without a PC, if there is a while(!Serial) in the sketch, it waits for the serial monitor and does not work forever.
Did you change the wiring to A0 to A2, and did you change the ADC input pin from A0 to A2 in the sketch?
The charge controller is an ETA4054, and the calculated value is 360mA with the set resistance R22=2.7k in the schematic, and the measured value is 370mA.
The solution to the problem of not being able to upload is on the ESP32C3 wiki.
For direct mail, click on my icon and then click on the message symbol and you will be able to write an email. But for anyone else having the same problem, I think it would be better to post it here.
edit:
I charged a 220mAh battery with built-in protection circuit as a test. The battery is charged at 370mA from XIAO. It seems that the protection circuit does not have a function to suppress the charging current to a safe value, and it is necessary to limit it on the charging circuit side.