Turns out there's a third option, sort of a "light" version of the first option. MacroDroid has a Weather trigger to trigger a macro if the weather has changed at the location stored in MacroDroid's settings (Settings > Trigger Options > Weather Trigger > Weather Location). If you're OK with seeing weather info from a relatively fixed location, the attached macro might work for you.
The macro displays the most recent temperature as a text notification, as well as the current weather condition as an icon notification.
You will need to create a Notification Channel called "FYI" for the notifications, but it's a one-time-only process. Go to Settings > Notification Options > Notification Channels, then tap "+". Once you create the channel, you can configure whether its notifications make a sound, or vibrate, or not, in Android's Notification settings.
The macro displays icons for clear, somewhat cloudy, very cloudy, drizzly or rainy, thunderstorms, or snow, or other. You can change any of the icons. FYI: the list of possible weather conditions is at
https://openweathermap.org/weather-conditions; MacroDroid coincidentally uses that same OpenWeatherMap.org API I'd mentioned in my earlier post,
If you travel a lot and need the weather info for the location of your phone to be updated a few times a day (more than you'd want to manually update the MacroDroid Weather Location), I can probably modify the macro pretty easily to utilize the API directly instead of using MacroDroid's Weather trigger.