Other than letting you watch linear TV anywhere you go, YouTube TV also allows you to save as many episodes and shows to a virtual DVR as you like. This likely helped grow many people's libraries to unsurmountable sizes, which makes it harder to keep track of what you've watched and what you haven't. Google seems to recognize this, as the company is starting to roll out a "mark as watched" option so you can manually sort out episodes you've already finished, in case the platform hasn't caught that you did.
Even though the feature isn't available for everyone just yet, YouTube TV's help page already tells us how it's done. To mark an episode as watched, long press it or tap the three-dot overflow menu next to the preview. There, you should find the aptly-named "Mark this episode as watched" entry. Tap it, and it'll look like you've watched that show. It will also automatically appear in your watch history.
The capability is currently rolling out, so it might still take some time until it hits your devices. Since it appears to come as a server-side change, there's no APK or Play Store update you can install to get it faster. If you like, you can still get the latest version from APK Mirror, though.
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