Oyster shells are not grit. They are not hard enough to grind up everything a chicken may eat but the main problem with oyster shell as grit is that the chicken's digestive tract makes acid, just like ours does. The acid will dissolve the oyster shell so it will not last to be used as grit.
Grit is just rock, from the size of a grain of sand to the size of a pea for full grown chickens. Chicks, not being full grown, can't use the larger pieces. Commercial grit is granite. Granite is hard so it lasts a long time and it is readily and cheaply available. They just screen it out from the debris from granite quarries. It is good recycling of a by-product of the quarrying process.
If chickens have access to the ground, they will usually find their own grit. If they are in an area where the ground is swamp muck or such that has no gravel or rock in it, they could have a problem, but in most soils they will find something to use as grit. That's part of why they scratch. They are not just mining for worms, they are also mining for grit. If they are confined to a small area, they will eventually find and use the choice chunks of grit. I see absolutely nothing wrong with offering grit on the side, whether they need it or not, either in a separate container or throwing ot on the ground where they get the fun of mining for it.
I personally don't like mixing grit or oyster shell with their food or mixing grit and oyster shell on the side. With me, it is always separate containers. They may be able to distinguish between feed, oyster shell, and grit when they are mixed, but why take the chance of confusing those adorable little birdbrains and causing them to eat more of something than they need?
Chickens will use any gravel or sand they find as grit. If the native rock is softer than granite, it gets ground up faster so they eat more of it. If the native rock is limestone, they get calcium out of that. Some chicken feed contains limestone to provide calcium and grit, though if they don't free range, I'd still offer grit on the side.