It’s a reasonable “heavy” game, that requires a decent phone. S8 should be good enough though.
In general, even on slow phones, once a certain environment is loaded, it’s smooth. If you start a darting session, there should be no lag. If your map is loaded, it should be smooth. Unless you travel fast.
A new phone will definitely get you a smoother experiences, since it’s new and clean and probably faster, but don’t buy one with an insane amount of RAM just because of that since the game never uses more than 2GB or so.
Currently using a Galaxy A50 which runs everything smooth, but it could be a bit faster. It’s a budget phone though.
My previous Galaxy A5 2017 ran smooth too, but everything had to load very long. From the moment you press Launch until you’re back in a loaded map took 50-60 seconds. Now it’s more like 40-45.
Also had an iPhone 6S before, that ran the game really smooth. Just drained the battery in an hour.
Anyway, I really think you underestimate what might be running in the background. It’s a very common misconception that people think that if you don’t force close an app, it remains active. In fact, it just stays in memory, once memory is required it gets removed from memory. It doesn’t really “do” anything when it’s not in the foreground.
Every app, however, has a number of services. Things like calling to servers to check for messages, or having an open connection for push notifications, or other things. These services remain active even if you force close an app. Even worse, they restart when you force close an app, using resources and draining your phone.
My professional suggestion: Never force close any app, unless it’s malfunctioning. Let your phone handle memory management, it’s very good at it.