I'm playing with a small private mod pack, in which Elytra Trims as well as Additional Banners and Archaeology Banners are included.

I decided to test around if Elytra Trims and both banner mods would work out of the box, but it didn't.
Not only that, but I tried to add the "elytra_patterns" sources in the "armor_trims" atlas, but I assume that just does not work this way?

So, is there any way to add modded banners using a resource pack, or does it need to be coded in? And if it's the latter, would it be possible to do that?

It should be possible, but for some reason it breaks on rendering. It will be fixed in the main mod, and compatibility resourcepacks will be added to the extensions

Will be in the next update 👍