Obviously it isn't just a pre-HD thing or something a lot of games of that era did. At the very least I see it as another example of them intentionally leaning into technical limitations for style points, just like the big random circles or leaf shapes instead of actual leaves here
Not even sure why it's hard to believe that these patterns, sometimes checkerboarding and sometimes literal weave textures, are intentional when Nintendo literally made a bunch of games with this style
Reminder Galaxy is literally a bedstime story, for that reason alone the bed sheet/plushie patterns are actually pretty fitting and not that random