Option to remove items from continue watching

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Workaround: mark the media as watched at the lowest level you're comfortable with. For movies, there's only one level. For series, you can mark the episode as complete, the season as complete, or the series as complete.

If you don't want to record that you've watched the media, mark it as unwatched immediately after. This discards your progress and ensures that "Next Up" doesn't populate with the next episode (or next season's first episode). Unsure how it interacts with systems like Trakt if you run those, but it works as a general solution.