Warning: My question contains some assumptions and mumbo jumbo. I attempt to learn how this stuff works and its correct terminology. And though I've implemented some of it (not all) from scratch over the years, I've done it my own way. As a result I'm sure I'm misusing some terms. Nevertheless I have partial technical knowledge of it whereas the web and YouTube if chock full of people attempting to discuss them with even less technical knowledge and misusing the terminology even worse than me. But here we should have some people expert enough to the field.
Affine transformations of bitmapped graphics can achieve scaling, shearing, and 2D rotation.
Homogeneous transformations of bitmapped graphics can additionally achieve 3D perspective mapping with foreshortening.
The Super Nintendo supported affine transformations for scaling and rotation in hardware, but also supported the famous "Mode 7", which could achieve perspective homogeneous transformations in the ground plane, X/Z, only (I believe) by cleverly adjusting the affine transformation a bitmap was undergoing on each scanline, the Y-axis.
The original PlayStation 1 only supported affine transformation which resulted in warped textures since affine transformations cannot do perspective foreshortening without clever tricks like that used by SNES Mode 7.
As far as I'm aware all the later consoles supported texture mapping with full homogeneous transformations and hence perspective-correct textures.
But for the Sega Saturn I can't seem to find good technical details. It could definitely do full affine transformations and apparently wasn't originally designed with full 3D texture mapping so many techniques were used to try to match the 3D capabilities of competing consoles of the day as best they could, to varying degrees of success.
So apart from any other limitations, could the Saturn do homogeneous transformations, only affine transformations, or could it achieve or approximate perspective correct texture mapping using some kinds of tricks similar to what the SNES did?
(I never owned any console but I did my own 3D graphics programming from scratch in the 8-bit days and affine texture transformations from scratch later on, but never managed homogeneous transformations from scratch.)
I want to include some diagrams to show the difference between an affine warp and a perspective projection. I haven't found good ones yet but while searching I realized that many images on the net labelled as "affine" are actually triangle based and show a warped square with the two triangular halves warped differently. This is what the PS1 does I believe since it was triangle based and this may cause people to believe this is what affine warping always looks like. The Saturn was quad based so will look different because although the texture won't be perspective-correct, it also won't be made of two mismatching triangular halves.
There's also the possibility of rendering a large area as a series of adjacent squares or rectangles, where the vertices of each will be correctly 3D projected but the textures within won't be. I have a hunch this may be what the Saturn did, which would result in less ugly warping that on the PS1, but more warping than on any of the later consoles.
This second image contrasts two affine-warped checkerboards. One made up of two mismatched triangles as the PS1 would do. The second rendered as a single affine-warped quad. Note that neither are perspective correct.
Here we have the 2D texture in the top left, the affine warped image made of two mismatched triangles in the top right, the affine warped image made of a single quad in the bottom left, and the perspective (homogeneous) projection in the bottom right: