You can add podcasts to Updates by tapping the + button in the navigation bar on the main screen. From there, you can browse or search for podcasts in Apple's Podcast Directory.
By default, Updates searches for podcasts based on your phone's region settings, but you can change this if needed.
If you have a share link to a podcast from another app, simply paste it into the search field, and Updates will attempt to find the podcast for you.
Note: You don’t need to add a podcast to play or bookmark its episodes. In the Add Podcast section, you can tap any podcast to view all its episodes.