How to have podcasts autoplay after the iOS 11 upgrade? So once a podcast ends, it doesn’t just automatically to the next episode anymore. Is there a way to get around this?
Yes. On 11.1.2 (maybe earlier versions as well, haven't checked), you can create your own station and the app will play the next one in the list after the podcast ends.

Example to autoplay all episodes of a single podcast:


In the "Library" screen of the podcast app, choose Edit -> New -> Name it something. 
Set Station Play to "Oldest to Newest" (to mimic play order of previous podcast app versions)
Set Include Episodes to "All Episodes"
Choose Podcasts -> the Podcast you want to auto-play.


Now play your new station and autoplay next will work.