I tried looking this up but there are only examples for previous versions of iOS where there was an option in the podcast settings called "mark all as played".
This option is not there anymore. Is it gone forever?
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Marking all podcasts as played
This feature was originally removed sometime during iOS 7 (I think iOS 7.1, but am not certain on this).
Just in case you're not aware, the closest option to doing this within the builtin Podcasts app is to do as follows:
This will mark all your selected podcasts as played.
Of course, you can also use iTunes to mark them all as played and then sync your iPhone, but that may only be quicker overall if you wanted to mark multiple series of podcasts as played. Otherwise the above steps will most likely be more convenient - although certainly not as convenient as the older Mark all as Played option in earlier generations of iOS.
In terms of whether this feature is gone forever, no-one here (or even at Apple) can answer that. There's no telling what may or may not happen with the Podcasts app in future.
Alternatives Finally, there are a number of very popular third party podcast apps which many users have turned to. It may be worth you investigating some of these to see if they're suitable for your needs. I list a few below (some are free, others aren't):
Note: I am not affiliated with any of the above apps in any way.