I enjoy exercise, but I don't see the same conflict as you do between engagement and distraction, at least within certain parameters. I listen to audiobooks or podcasts during my long runs and easy runs, which are on the paved river path or lightly-traveled roads. I listen to nothing or to familiar music (I think familiar music is different from unfamiliar music in terms of attention needed) for workout-runs, e.g. intervals; music makes me a little faster because of the fast beat, I think. I listen to nothing when I trail run, because I enjoy being immersed in the experience of the trails and scenery.

The thing is, I think that during outdoors exercises, attention paid to surroundings is still attention not turned inward to the exercise. So I'm not sure I'm more fully engaged in running when I'm trail running and looking at the mountains, vs pavement running and listening to a podcast. But when I'm doing intervals or harder efforts, I want to be focused more on my running, so I do those on familiar territory (or on a track, which is boring!) and with no audio distraction.

(But running is easy, mechanically. I see people mountain biking with headphones and I can't imagine! Mountain biking takes all my attention - sometimes I can't even look at the scenery because I'm too busy trying to make it around switchbacks or over rocks without falling over...)