EZData is just one of the possible data storages. With M5 products it is very easy to use. It is also possibe to use other cloud services. Cloud means "some storage somewhere on the internet". It requires a connection to the internet anyway.
- Use a separate non interupted connection such as LoRa or mobile internet for your battery measurement. Depends on what is possible at your location and what/how you need to communicate.
- log to a cloud like storage in the local network, powered by battery on mains loss. No access during power loss but all data saved
- Detect the internet connection loss and log to SD card until the connection is back, then upload all missing.