Smaller phones do have a place though. I’ve got a 7-year old son with Type 1 diabetes. We wears a Glucose Monitor that requires a Bluetooth connection to get a reading. He needs to carry a mobile phone for this reason, and because of his size, and the fact that he needs to carry it basically all the time, a smaller phone is best. He does not need a camera, or to browse social media.

This app: https://play.google.com/store/apps/details?id=com.samruston.weather when I had it installed has an option to make the weather notification permanent (persistent).

This app seems to have been sold since I last installed it.

I don’t think you can get widgets on the usual Android lockscreen anymore. What I used to do was make the weather app have a persistent notification, and have that notification showing on the lockscreen.