I quote the Wikipedia page for this show : "Super Show would also feature additional live-action storylines following the Mario Bros. at their plumbing business in Brooklyn, and once per week would replace the usual animated Mario segment with one based on The Legend of Zelda "

Consequently, they are part of this show and not a separate one. The other show is going to be deleted.

Would it be at all possible to appeal this decision? The Super Mario Brothers Super Show and the Legend of Zelda were commissioned together, and the cancelation of Super Mario Brothers Super Show meant that no further episodes of the Legend of Zelda were produced beyond the initial 13, but the shows are entirely distinct as pieces of media. The have entirely different settings, characters, production staff, etc. The Legend of Zelda has also been released separately on VHS and DVD.

It is not possible to cohesively group the Legend of Zelda with the Super Mario Brothers Super Show because, besides being commissioned together, they have nothing in common. Indeed, other outlets make this distinction - The Legend of Zelda is not placed within the Super Mario Brothers Super Show on Amazon Prime (see https://www.amazon.com/Legend-Zelda-Season-1/dp/B004M86ZS2), or Apple TV (see https://tv.apple.com/us/show/the-legend-of-zelda/umc.cmc.2gr5xc4ojnwpy5ozckmgt1uj6), or IMBD (see https://www.imdb.com/title/tt0832330/), or TV Guide (see https://www.tvguide.com/tvshows/the-legend-of-zelda/episodes-season-1/1030453845/). I don't doubt that I could find even more examples, but I feel these four are sufficient to make the point.

For all our listings, we are going as per the original broadcast, which was done as one single series. The fact that they are now released separately on DVD or digital services has no impact on our listing.

The episodes are still available here, with their Super Mario Bros original intro.

This is the same, for example, that The Ant Show, which was also originally made of unrelated segments which are now also released separately.

I'm afraid I may not understand. Are you describing shows that aired side-by-side, or shows that were produced alongside each other? With The Atom Ant Show being an example, Atom Ant initially aired together with Secret Squirrell and Morocco Mole as The Atom Ant/Secret Squirrel Show, if I recall correctly.

The Super Mario Bros. Super Show! was made of 2 segments Super Mario and The Legend of Zelda.
The Atom Ant Show was made of 3 segments : Atom Ant, Precious Pupp and the Hillbilly Bears.
The Secret Squirrel Show was made of 3 segments : Secret Squirrel, Squiddly Diddly and Winsome Witch.

The fact that the different segments are now considered as separate series has nothing to do with our listing.