A typical quake style FPS netcode like Counterstrike, Apex Legends, Titanfall etc. would have all gameplay affecting objects (bullets, missiles props whatever...) as server side entities.

On the client these entities are usually interpolated, except the local player character, which has client-side prediction (eg. optimistic execution with rollback to apply server corrections to maintain server authority).

So it's not at all unusual to suggest that all gameplay affecting objects would be server-side. In this network model, that is the default approach.

The exception would be for entirely cosmetic FX or cosmetic debris objects that don't push back on the player.