As can be seen, I have curios at a higher version than needed, but the way it's written Botania isn't liking it.

This same issue occurs on the 1.16.2 version of Botania(405) as well, I tried downgrading to fix it, as I am on 1.16.1, but that did not solve the issue.

How is this an issue? 3.0 is newer than 3.0-beta4.
https://www.curseforge.com/minecraft/mc-mods/curios/files/3011016

Did you by any chance get confused by Curseforge's awful UI? The files tab is generally much more useful, the main page only shows one of each: release, beta, alpha.
Also, maven version comparison will take a version without a qualifier as a newer one than with one. Forge uses Maven's version range implementation for this. Maven docs

For 1.16.2, use Curios for 1.16.2.