Can I play my downloaded podcasts through the Apple Watch speaker? What can I play through that speaker?
Hi
Podcasts are not compatible with the built-in Music app (which also does not play music through the watch's speaker).
You can play music from your watch after you have paired it with Bluetooth headphones.
More information: Listen to music on your Apple Watch - Apple Support
After reading the Apple Support document, it is not clear to me whether I can listen to the playlist through the paired headphones only, or through the headphones OR the Apple Watch speaker.
You cannot play music through the speaker (whether before or after pairing headphones).
If you would like to suggest that Apple considers adding that as a new feature, you can do so here (all submissions are read, although you should not expect to receive a reply.):
What can I play through the Apple Watch speaker?
