I stopped wearing headphones while running when the pandemic started. I really don't think about much. It's become sort of meditative for me.
I do sometimes find I come up with good ideas for work/whatever when running, so it can be a good way to ponder things like that and I’ll sometimes record a short voice memo on my Apple Watch otherwise I forget what I thought of. But after 20 minutes or so I find my mind kind of defaults to blank and I like that!