This is by design.
First, understand the new feed url is supposed to be set on the old feed, not the new feed. I assume you are moving from WordPress/PowerPress to some other platform. If you're moving from some other platform to PowerPress, then you need to set the new feed url on the old platform your moving from.
To clarify, example.com/feed/podcast/ is a podcast channel feed provided by PowerPress by default.
IF it's a category feed, enable category podcasting, then go into PowerPress > Category Podcasting, edit the category in question and set the new feed URL.
IF it's a channel feed (as from your example), enable podcast channels, then go into PowerPress > Podcast channels edit the channel in question (default podcast channel is example.com/feed/podcast) and set the new feed URL.