Wow, thank you for saying exactly this, this "deferred anxiety" probably does partly explain sleep issues I've had the last 3-4 years. I agreed with GP's comment and have more issues with screens, but didn't even notice this difference in how I take my walks now.
Sometimes my inner thoughts can crowd aside the podcast and I'll get home and realize I didn't hear anything from the podcast, but more often it keeps me distracted the whole time. I think unplugging from podcasts on walks and in the car is definitely worth a try.
Walking and movement is supposed to be a massive help for sleep, but in periods where I have more anxiety, this effect is stronger than the benefits of the walk itself. I manage a quite decent hygiene around my phone use, but buying in-ear headphones was quite a mistake on my part, as I found this difference quite soon after.
Sometimes my inner thoughts can crowd aside the podcast and I'll get home and realize I didn't hear anything from the podcast, but more often it keeps me distracted the whole time. I think unplugging from podcasts on walks and in the car is definitely worth a try.