Introduce button for "Mark Played and Delete" in selection menu
It requires two long presses to mark an episode played and delete it currently.

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Jonathan commented
Currently we have the "Delete downloaded episodes when you mark them as played manually" option which provides most of the benefits requested here. However, IMO it would be improved by having these deletions respect the "Move to Recycle Bin" setting as well (that is, marking an episode as played would move it to the recycle bin rather than deleting it immediately).
I routinely decide to skip automatically downloaded episodes by marking them as played and deleting them, but I prefer them to always go into the recycle bin so I can easily restore them if I change my mind shortly after.
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Anonymous commented
yes please, would love an option to delete when episode is mark played, one less step.