The GBA version does actually leverage dynamic polygon splitting in direct reference to how PS1 games used this approach https://www.youtube.com/watch?v=1Oo2CZWbHXw&t=271s

I think the resolution makes it particularly rough though.

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.