ESP32 in deep sleep modes is reasonably battery friendly (all depending on your frame of reference, of course.) 5uA in RTC-only and 10+ uA in RTC+ULP sleep.
Presumably for a watch use case, you'd plan to deep sleep (ULP) or hibernate (RTC) 98+% of every minute and turn the radios on as infrequently as you could stand to get external notifications. I don't need split-second precision on my notifications if the alternative is a much longer battery life.
You can use the ESP32 onboard RTC to do periodic wakeups. (You can also use external stimuli via GPIO pins, but you don't need anything extra if all you want is a periodic wakeup.)
