You can now archive a podcast you're pausing or no longer actively producing, without unpublishing anything. Open a podcast's actions menu and select Archive Podcast. Its website, RSS feed, and existing episodes keep working exactly as before; archiving only clears it from your everyday view in the Studio.
An archived podcast drops out of your active Podcasts list, the podcast picker when creating a new episode, and the picker for a new automation. Automations already running against it keep going. Unarchive anytime from the actions menu, or from the notice that replaces the episode composer on an archived podcast's page, to bring it right back.
To find an archived podcast again, or just get a better view of a growing list, the Podcasts page has a new filter icon next to Create New Podcast. Status switches between Active (the default), Archived, and All. Sort by switches between Episode Count (the default), Recent episodes, and Alphabetical.
See Archiving a Podcast for the full walkthrough.