One idea might be on deep sleep exit function to measure the battery level (supposing the hardware allows you that). If lower than a still safe lower limit (e.g. 3.1 V) disable deep sleep exit event.
But this will still require some external event when battery is back charged.



The hardware ...

I have built a battery(li-ion) powered product around the ESP32-MINI-1-H4.
I did not include a reset button, thinking it would not be necessary. There is no hard shut-down either. Shutdown of the product is handled by sleep mode.

When the battery is discharged below ~3V, brownout reset is triggered ...

Can I please see your multiapp bootloader?