Picos are very bad for battery applications. If you do end up doing this, make sure it is mains-powered like your original thought.

Esp32s, MSP430s, and nRF chips have sleep currents down to around 5uA or less.

Picos have sleep currents of 1-4mA. That is 1000x higher and the battery will only last for a few days instead of a few years.