The sharing pages also display badges for listening in specific podcast apps for listeners who want to listen to the rest of the episode, including Overcast itself (strictly optional) and Apple Podcasts.

This won't help much if you're trying to capture the entirety of a segment, or if there's tweaks you'd like to make to the audio or picture quality. Even so, this might be a boon if you're determined to share a hilarious or insightful moment and don't have the experience (or inclination) to produce a bite-sized clip in another app.