> I don't care about winning or losing. But I don't know how to say, "whatever, moving on" in a way that itself doesn't get interpreted as further pettiness.

I struggled with this for years. In the end I just settled on saying "Respectfully, I think we will need to just agree to disagree. No hard feelings." A few times I've had to drop the "This conversation is going nowhere good. Let's talk about something else."

Being direct is under-rated. I find people aren't offended when you do it, as long as you are maintaining some basic amount of social decorum / grace.