Not in my experience.; in small towns, you get to know everybody. In big cities, you pass through the streets like a ghost unless you make a real effort to escape your comfort zone. Move to a little town, and you're forcibly escaped from your comfort zone as soon as the clerk at the grocery store sees you twice and starts a conversation with you, and you find out his wife is one of your kid's new teachers.
I did both, moving out of a big city in middle of pandemic. Socialization became 10x easier the moment I moved. Anecdotal etc etc, but people are more friendly and more outgoing where I moved vs where I moved from.