ESPHome is really cool, but it's still missing power management last I checked, which is the main reason I don't use it these days.
I'm not sure why enabling automatic light sleep isn't like, priority #1 for Arduino, but I guess there's some subtle issues where it might break certain sketches or something.
Because realistically none of the hardware used even supports deep sleep correctly and will drain the battery using their high quiescent current LDO regs, pull-ups, LEDs and vBat dividers. Also latency and energy cost of getting back on the network, waiting for hass server to connect (in esphome protocol devices are servers, not clients) and going back to sleep is only going to work for some weird edge scenarios where you don't care about latency or polling rate.
Automatic light sleep maintains a WiFi connection with only 1 or 2 milliamps, I'm using the exact same ESP as server model but with Websockets, and it all just works.
There's even some PRs for automatic light sleep I think in ESPHome, but they're not merged yet.
I'm not sure why enabling automatic light sleep isn't like, priority #1 for Arduino, but I guess there's some subtle issues where it might break certain sketches or something.