Where is this "Up Next" playlist that my podcasts are saved to?

The Up Next list is rather bizarrely buried, and not that useful once you find it.

1. Start a podcast playing.
2. You should see a small "mini-player" bar across the bottom of your screen. Press that. It'll expand to give you a full-screen player.
3. Look towards the bottom right corner: you should see an icon with three bulleted lines, with the bullets on the right side. Press that.
4. There's your Up Next list! Note that, annoyingly, you cannot actually do much of anything with this list. You can choose different episodes and start the Up Next list from that point - but you can't erase, or rearrange, or do most of the things you'd want to do.

To play the podcasts in the order you want, you probably need to...

1. Go to the "My Podcasts" tab.
2. Press "+" in the upper left corner to add a new station (i.e. a smart playlist).
3. Set "Include all Podcasts" to all (or whatever).
4. Select Station Settings, and choose "Play" [order] to "Manual", "Episodes" to "All Episodes", "Unplayed Only" to on, and "Group by Podcast" to off. That'll give you a playlist that includes all your unplayed podcasts. You can edit that playlist to drag and drop the episodes in the order you want, although unfortunately any new episodes will automatically go to the top of that list.

This app is a mess.

Up Next is one of the most important features of a podcast app.

You need to have something playing AND you have to press 3 unintuitive buttons to get to the list?

This is garbage. Gonna go download another app.