I updated both of these devices to iOS 15.5 last night. Ever since, I cannot play any podcasts. I press play but they never start actually playing. Music works fine. Podcasts still work on the Xbox app. This must be a bug or something. I restarted both devices and deleted/reinstalled the Spotify app on both, to no avail.
edit - it seems that the issue is limited to 2 podcasts. Others seem to work fine.