Shader: How to write a shader that respects sorting order first and then depth

This is not possible with pure shaders since your screen only has a single depth buffer, Either your shader uses the depth buffer or not. What you would need is clearing the depth buffer between your "order" layers. This could be achieved with a custom scriptable renderpipeline where you can introduce as many intermediate steps as you want. Though keep in mind when you clear the depth buffer, things drawn afterwards can not be occluded by geometry rendered before that.

A simple solution if you have just two "layers" is to simply use two cameras and let the second one render only those objects that should appear on top of everything else. The second camera should only clear the depth buffer. This is commonly used for FPS games to render the local weapon model since we don't want the weapon to clip into world geometry. Though if you want to have many layers that behave like that, you would need to implement a custom renderpipeline.

That's all not really trivial. Also keep in mind that opaque geometry behaves very different then transparent geometry. Opaque geometry is usually sorted front to back while transparent geometry needs to be sorted back to front.