Compasses you add aren't actually new items. Instead, compass type is stored in a data component.
Warning
This means that recipes for inexistent compasses will still work and display in recipe viewers.
Simple Shaped Compass Recipe
Compass recipes use a components object to set omnicompass:compass_type to the right compass type.
The following recipe uses a compass and planks and creates a biome compass as a result.
{"type": "minecraft:crafting_shaped","category": "equipment","key": {"C": "minecraft:compass","S": "#minecraft:planks"},"pattern": [" S ","SCS"," S "],"result": {"components": {"omnicompass:compass_type": "minecraft:biome"},"count": 1,"id": "omnicompass:compass"}}