Affine texture mapping is kinda jarring to look at, especially in this GBA port since there is no fixup with huge ground polygons drifting around.
One of the listed features in the PS1 port in the OP article is tesselation to reduce the issues of the PS1 HW affine texture mapper, on the GBA you have some base cost of doing manual software texture mapping but also oppurtunities to do some minor perspective correction to lessen the worst effects (such as doing perspective correction during the clipping process).
Almost felt like the second video (despite being older) looked better in terms of texture jumping, looking closer now the wandering textures actually seems more to be more of an clipping issue than directly perspective correction related.
You’re misremembering. SM64 was fully textured, outside of specific models.
Also flat shading (vs. say gouraud shading) is isomorphic to the question of texture mapping, and concerns how lighting is calculated across the surface of the polygon. A polygon can be flat shaded and textured, flat shaded and untextured, smoothly shaded and textured, or smoothly shaded and untextured.
Still bravo! I know getting it working and complete is the real goal and it is commendable.