Apple has introduced a new feature for Apple Podcasts in iOS 17.4 that provides a transcript for seemingly nearly every podcast.
Machine translation has improved significantly in recent years, to the point that spoken word should be relatively non-trivial to transcribe into text. Apple's work on machine learning models and artificial intelligence has led to a new feature for Apple Podcasts.
Users testing iOS 17.4 beta 1 have discovered nearly all of the podcasts in their library show transcripts. There seem to be some that don't, and any added from an external source like a URL won't.
The feature is new and still in beta, so there isn't any information on implementation or expected accuracy. Users should expect most, if not all, shows delivered through Apple's podcast network to be transcribed.
Limitations and other details will likely be shared by Apple once iOS 17.4 is released to the public in March. The update is primarily focused on updates pertaining to EU regulation.