What staff told you is correct. I set it through the mobile main page a few years ago. Originally the search results there were taken from Promote. Then that feature broke.
When promote on the mobile main page was introduced, my memory is that the text/image should have been populated from the old Promote feature where possible. The results were a bit haphazard. I think think the image could have been anything from a badly stretched visualization image to Wiki.png to a fandom logo. I remember I was helping another wiki with theirs and decided to check ours. I can't remember exactly what was there, but it was broken. So I reset it; and for lack of any better options I probably just decided to resize the main page slider image to fit.
I like the new one you chose.
In terms of the text... does the current search result match what you found on the mobile page? It doesn't now, but I don't know if you changed it. I suspect it was originally from the Promote page.
Yeah, there's no history for mobile changes (in contrast with the spirit of a wiki), so there's no way to see what came before.
I haven't changed it, but the mobile description currently reads "Muppet Wiki is a collaborative encyclopedia for everything related to Jim Henson, Sesame Street, and The Muppets."
While the search results on community.fandom reads "With more than 25,000 pages and 75,000 pictures, Muppet Wiki is a collaborative, comprehensive encyclopedia for everything related to Jim Henson, Sesame Street, The Muppet Show, and the Muppets Studio. We have pages for the shows, the movies, the characters…"
Then likely I tried to change it at the same time as I uploaded the image (I can't imagine anyone else ever did). Assuming I changed it at the same time as the image, "heavy caching" would be a distinct understatement.
Search was originally pulling from Promote directly; the mobile main page section was an attempt to give admins a way to change it again.