In the original Halo Reach on Xbox 360 the armor effect equipped on your spartan would also show on your elite, this was literally the only extra layer of customization elites had in the game’s multiplayer, severely downgraded from Halo 3, before of course disappearing entirely in subsequent entries.
This I believe is a known issue, but might still be worth filing a bug report about this on the Halo Support site: https://aka.ms/HaloSupport
Be sure to read over the known issues list first before reporting. Going to close this off as it’s not a support issue