Vulkan: Alpha scissor/test material has pixel Z-order issues

[Zylann]

Godot version

4.0 ed395c6

System information

Windows 10 64 bits GLES3 GeForce GTX 1060 6GB/PCIe/SSE2

Issue description

When I use an alpha clip material for foliage, I expect it to behave like an opaque material, going through the opaque rendering pass, so it should not have Z-ordering issues in its pixels. However it looks like it does have that typical issue:

Steps to reproduce

1. Create a mesh made of two intersecting quads (or make two separate quads), typical setup for classic grass
2. Create a new StandardMaterial3D with transparency set to Alpha Clip and an albedo texture.
3. Assign the material to the mesh instances.
4. Observe they completely disappear with Vulkan errors. I assume that's a different issue. Close the scene and reopen it. Observe the clipping issue.

Minimal reproduction project

AlphaClip.zip

[TokisanGames]

The MRP can no longer be opened in Alpha13. However Alpha Scissors no longer has this issue with z-order. There are other z-order issues in the pipeline and I'll open another ticket, but it's no longer present here.