Anyone who has ever been a local knows that locals spend time living their life; they rarely go to museums, etc in their own town; and if they do they probably go to specific ones multiple times (the ones that go with their hobbies, say).

There is something to "not being a stereotypical tourist" but that's easy enough to do by being polite, and paying attention to what is going on, and wandering off the beaten path now and then.

Visiting off-season can be a great deal, especially if you're not concerned with weather (for example, if you're going to be visiting museums in Rome, they will be open during the rain as well as the shine).

I'm very aware of the nature of my relationship as a tourist, but I do want to be an active participant and not a passive observer.

I mean looking around where I live (a quiet, fairly middle class suburb), I'm sure they would get bored pretty quickly. There's no stores or landmarks here, just some playgrounds and bits of greenery. People live here, they do business and entertainment elsewhere.

"Living like a local" in most places means spending the majority of your waking hours working to pay rent and much of the rest of it doing household chores, and your rare trips out being more likely to be to McDonalds than to enjoy the local cuisine...

That's how I like to travel. Stay with someone, help with their chores, go to work when they do (the benefits of WFH), basically mirror the life they live. Those rare trips get compressed somewhat, largely because being able to share the experience with the host means that there is greater desire to make those rare trips happen while I am there as a guest, but not excessively.

There used to be (maybe still is) a pretty robust couch surfing crowd in the days before airbnb. I did a decent amount of traveling that way in my 20s around the world and was able to accomplish this that way. Good times.