I'm not entirely sure how this could be done easily, given every mod seems to use different tags for their chests, but to use an example, SimpleBackpacks seems to accept BetterEnd chests despite them using different tags as far as I can tell, and not having any explicit integration between the two mods, however Adorn checks very specifically for just vanilla chests, not even using a tag, so they're completely incompatible.

Some Fabric mods with chests that don't work in Adorn recipes include:
-BetterNether
-BetterEnd
-Bewitchment
-Charm
-Sakura Rosea

I've seen the exact same occur in the forge version of Adorn.
Some Forge mods which add their own chests include the following: (Quark/Charm have forge versions)
Quark, Charm, Terrain Incognita, Autumity and Environmental.

This is probably easier to fix on Forge. I'm not sure if there's a standardised tag for these on Fabric (though #c:chests might be), but Forge likely has something like #forge:chests.

It has forge:chests and forge:chests/wooden. I think the forge:chests/wooden one only looks for wooden ones whereas forge:chests will use any available chest.