I actually posted a thread asking the same question not long ago. Nobody said that villagers have ever shown up at their house or asked to visit it. Sometimes villagers mention wanting to go to your house but so far nobody I have heard from have experienced villagers visiting their house.
I was wondering this same thing! I get all excited about villagers saying they want to come over but they never seem to in the end, I haven't had any experience just yet that has resulted in this happening
I do not think it's a feature that's available in this game sadly. They don't ask to come over which includes setting up an exact time and them showing up at your house like they did in NL. The closest thing to this, are villagers sending you letters about hanging out sometime soon. But nothing really ends up happening.