Caelus API Do I Need This?

Yes - if another mod relies on it. Caelus API is a required dependency for mods that move elytra flight off the chest slot or grant gliding from new sources - extra equipment slots, trinket/back slots, capes, wings, or status effects. Those mods will fail to load or lose their flight ability without it.

No - on its own. Caelus API by itself does nothing visible in-game: it adds no mobs, blocks, items, recipes, or world content, and it does not give you the ability to fly just by being installed. There is nothing to "use" directly as a player.

Rule of thumb: if your modpack or a mod lists Caelus API as a requirement, it needs to be present. Otherwise it serves no purpose alone.