Re: I have almost 250GB of free space on my phone
Good.
(Any space you may have in iCloud doesn't count ... it is the storage space available on iPhone itself that counts.
ie: Settings > General > [Device] Storage. )
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You may want to check which settings you have in place:
See: Change your download settings for Podcasts on iPhone - Apple Support
Eg: says:
"Podcasts you follow are automatically downloaded to your Apple device. Episodes you’ve played are automatically deleted from your device. You can change these settings, and adjust other download options".
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Also: Are you saving downloaded episodes ?
See: Download, save, and remove podcast episodes on iPhone - Apple Support
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Else: if you suspect a bug in the app itself:
You can always send feedback to reach those who work on the software behind-the-scenes at Apple. Although they will likely not reply, and it won't help immediately, if others are also experiencing similar issues, Apple may address that in a future update.
Web-form for Feedback: Feedback - Apple Podcasts - Apple