Very interesting - thanks for that.
This is consistent with my theory - at home, your 5G phone does not see any 5G signal, since it sounds like there isn't a nearby cell tower that sends it to your area. So when at home, your phone only sees 4G, sees the network extender, and then connects to it.
And then when you're in a city, it does see a 5G signal and connects to it.
So it really seems to me that when I'm at home, there is enough of a 5G signal, even though it's weak, that the phone's OS prioritizes connecting to a weaker 5G signal over a stronger 4G signal, and so it usually doesn't connect to the 4G network extender. Randomly the 5G signal in my home drops low enough that it then connects to the 4G network extender. But when the 5G signal randomly increases in strength, it then because it prefers it, it then connects to 5G, dropping the network extender connection.