You can play podcasts on your paired iPhone, paired Bluetooth headphones or speakers, or the Apple Watch speaker (supported on Apple Watch Series 10 and Apple Watch Ultra 2). See on your Apple Watch.
Do one of the following:
Stream a suggested podcast: On the Home screen, scroll down, tap a category such as More to Discover, then tap an episode.
Stream from your podcast library: From the Home screen, tap on your Apple Watch.
Navigate to a list of episodes: From the Home screen, tap
Play the current podcast.
Do any of the following:
Connect a Bluetooth device: Tap AirPlay, tap Choose a Device, then choose a Bluetooth device.
Connect an AirPlay device: Tap AirPlay, tap Control Other Speakers & TVs, choose a device such as a HomePod, then choose a podcast to play.
Open the podcast queue: Tap Playing Next.
Adjust the playback speed: Tap Choose an audio destination on Apple Watch