I use WiFi at home and friends.

This is the part I don’t understand. Mobile data would work in your houses too, right?

Further, in recent versions of Android, factory settings are set to automatically turn WiFi back on if turned off

I haven’t seen this happen, but I use MIUI (Xiaomi’s Android ROM) which tends to be aggressive in limiting battery use. It will actually cut hotspot if unused for a few minutes.

Am I the only person who switches off the WiFi after use? I thought that was common advice to save battery.

Android phone collects every WiFi network it has ever seen and sends it to Google

Possibly, but how often do you use WiFi on a phone?