I used an OpenWeatherMap key in my name a long time ago on my laptop and conky – I think I could adjust the polling to 1 call every 2 minutes that would be 720 calls a day if on 24 hours?
I also used my key in the /e/ widget; at a time when the widget was unstable for many users. Fundamental /e/ changes happened since, so I do not have that issue any longer and do not use the key.
The “new api” is a big advance (and seems a little intrusive in permissions, perhaps) and seems to allow OpenWeatherMap to involve: Pricing - OpenWeatherMap.
As I understand it the default weather widget uses /e/'s own “collection service” from OpenWeatherMap. On my Samsung the Widget “just works” I use no key of my own.