Hi,
Coding is not a problem, that's my territory, I'm just new to the hardware side.
One possible solution I thought of (don't know how good is it) is to just do everything with software, e.g. put the MCU to sleep to conserve power (though I think it would still need around 3V to do that), and periodically wake it up, then measure the capacitor's voltage with analog inputs, and promptly go back to sleep if it's low. Since it's behind the booster, this could possibly work, though I imagine the power losses would be large while doing all this. And I don't know yet if Arduino can sleep for a specified time, or does it need an external interrupt to wake up.
I'd appreciate more knowledgeable advice