how feasible would it be to give gems forge tags based on their rarity? this would allow gems to be sorted by their rarity using a forge tag.

Example : chipped ballast gem could get the tag apotheosis:gem/uncommon and another mod could then filter them out to be trashed as currently all gems only have the tag apotheosis:gem making filtering difficult as you have to manually add each gem.

Not feasible at all. Tags are per-item, meaning they cannot account for NBT. You can use a mod which supports NBT filters to manage them.