Many people think an unlisted YouTube video can only be watched by someone who has the link. That is only true while the video is in no public playlist. Once an unlisted video is in a public playlist, anyone who opens the playlist sees it, and it can show up in YouTube search.
An unlisted video stays in every playlist it was in before you unlisted it. YouTube does not remove it for you. According to YouTube's privacy settings documentation, unlisted videos:
This is how old and replaced videos end up in front of viewers. A viewer browsing a playlist sees an outdated version, or the same video multiple times, which looks unprofessional.
Playlist: SSW Tech News
❌ Figure: Bad example - Bad example - Unlisted 'zz' versions are still in a public playlist, so viewers see the same video three times
When you unlist a video, also remove it from every public playlist. This is part of the YouTube 'zz' process for replacing a video with a new version.
If nobody outside the team should see the video at all, set it to "private" instead of "unlisted". Private videos can only be seen by you and the people you choose, and they can't show up in a public playlist.