I don't run as much as I used to but empathize with this. It's fine to mix it up too. When I was doing longer runs I'd listen to a long podcast.

With weight lifting and higher intensity exercise I make a point to not listen to music to build up a tiny bit of mental toughness and be stuck with The Suck and also myself. Music is a crutch.

I do listen to music cached on my Apple Watch every now and then, but I got it primarily for quick voice note taking. Many an idea - most bad, some great - were birthed from The Suck.

Same. I do not now what the definition of meditate is, but I imagine I come close to it while running.

I don't run but I do a lot of walking. My mind wanders a huge amount during my walks, which I find nice. I am usually so focused on preventing my mind from wandering, even in leisure activities, for example by focusing on a movie or book. Sometimes I stay up later because it means I'll fall asleep quicker and not be alone with my thoughts waiting for sleep for as long. But I think there's a definite need in the human mind for time to sort things out internally, even if (and maybe especially if) there's thoughts you're trying to escape from.