I also don't think it's too unreasonable to use a C3 as an MCU in settings where a radio isn't required. The IC itself (aka not the wroom module etc) isn't that much more expensive than equivalently specced MCUs without a radio, and if you're already more familiar with developing for the ESP software ecosystem it might well be worth the few pennies extra. The ESP32-C3FH4X (so the IC with 4MB onboard flash, super easy to integrate into in a design) only costs $1.6 per unit on LCSC for 100 units (and mouser etc is similar).
This is exactly a thing the ESP32 with WiFi cannot do if powered by a standard alkaline battery. The battery would drain in a couple of weeks.
And on top of that, it probably doesn't work at all, as it cannot even send once because the peak power draw is too high for an alkaline battery.