Why does the ocean have layers?

Why does the ocean have layers?

I think I understand the basic answer; ocean layers are defined by differences in temperature and salinity that result in different densities, and I get that denser stuff sinks.

But I want to know more.

AFAIK, temp and salinity are not constant within a layer, and they smoothly and slowly vary with depth. Then, you get an extremely small buffer zone between layers, where temperature &/or salinity change rapidly, and then you enter a new layer.

But like, why? I get that oil will sit on top of water due to its lower density, and I get why oil is attracted to oil and water is attracted to water and why they aren’t attracted to eachother, and how that means that they wont mix. But I don’t understand why salt water and slightly saltier water won’t mix, I don’t get why the salt doesn’t diffuse in such a way that it smoothly varies with depth. Also, I get why it’s colder deeper in the ocean (with some exceptions, like near the poles, and near the ocean floor sometimes), but I don’t understand why temperature changes like a step function instead of something differentiable.

Right now, my best guess is that the temperature+salinity combination that exists between layers are somehow intrinsically unstable, but I have no idea why that would be.

Can anyone help clear up any misconceptions I have, and then explain what’s actually going on here if that question still makes sense after the misconceptions are cleared up?

Edit: is there a reason I’m being downvoted?