On the Google Podcasts website, there is a horizontal scrolling carousel at the top with the shows you have subscribed to. The Subscriptions page below now shows a list of the most recent episodes of the shows you have subscribed to, starting with the most recent ones. The release date appears with the artwork and the title and description of the episode.
The flow of the subscription is very similar to that of the mobile application.
This change now seems to be available to most people, which is a good thing, because it seems to be a rather elementary characteristic that probably should have been there from the beginning. If you’ve been waiting to see the latest episodes of your podcast subscriptions, you should be able to see them on podcasts.google.com/subscriptions.