It doesn't help that that there has been some shift of word meanings, desktop case used to mean horizontal case, now it means virtually anything that needs a monitor and keyboard plugged into it, whether it's mini tower, mini ITX, mid tower or full tower, or actual oldskool desktop. Also last two years, the "great unwashed" are calling anything that has full height expansion slots a "gaming computer".
Added to that, the mostly Asian manufacturers seem to have dropped the use of the word case, and tend to use the word chassis, so using that word can get you warmer.
Listicles that might be worth looking at ... https://whatintech.com/horizontal-pc-case/ https://tip-topreviews.com/15-best-horizontal … -cases-in-2021/ https://www.thecrazybuyers.com/best-horizontal-pc-cases/
Then you've got some manufacturers incorporating horizontal features into "mini tower" designs so those get missed... https://www.yycase.com/Mini-Tower-A2-Series.html
Yes you can go vintage, but I'll warn you, most of them only cope with about 30 or 40W of power dissipation, even the later ones. I've had two AT and ATX horizontal cases I tried to run K6-2 systems in, 400-500Mhz, and in all four cases (situations and literal cases) heat was the enemy, couldn't really vent them enough to avoid heat soak catching up with it within about 2 hours of hard use. The most successful iteration, I had one 50cfm 80mm in the back panel hole, blowing out, one 50 cfm intake in the front, behind the card supports, intake, and 3x35mm ziptied together in the bottom drivebay, intake. Plus the PSU fan was upgraded from a ~20cfm to a 40. ...None of those were very quiet... and I could maybe play 4 hours on that before it bombed... and that was starting at 21C ish room temperature, if it was 27C or so you didn't get much longer than an hour.... it would browse all day though. .. I gave up after a couple of years of trying and went to a mid tower.
I think what happens is, you pretty much always pull the hottest layer of case air into the CPU fan with a horizontal case... so if it's sorta stratified with a delta of 10C you're always feeding the 31C air to the CPU, whereas with a mid tower, you've got it halfway up the case, and get a stronger updraft effect, top to bottom, worst case when the air is dead you're only halfway up the 10C column, 26C, but I think the air moves better and you're probably a couple of degrees lower.
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.