Shadows not properly rendered from OmniLight3D when using vertex shading

### Tested versions

- Reproducible in v4.4.dev3.official [f4af8201b] Not Reproducible in v4.3.stable.official [77dcf97d8]

### System information

Godot v4.3.stable - Windows 10.0.22631 - Vulkan (Forward+) - dedicated GeForce GTX 1060 with Max-Q Design - Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz (12 Threads)

### Issue description

Upgrading from 4.3 to 4.4.dev seems to break omni light shadows

Building the scene from scratch in a new project has the desired effect:

### Steps to reproduce

I created a scene with 2 boxes (1 with faces flipped and 1 wish shadows only) inside an existing project and that new scene had omnilight shadows that behaved as expected in 4.3. Upgrading the project to 4.4 causes the lights to break. It's worth noting that creating a fresh project with just the scene shown above and upgrading that to 4.4 does not seem to create the issue.

### Minimal reproduction project (MRP)

N/A
I tried to create the scene described above in a new project but it succeeded.

Start by comparing the existing-project upgrade path from Godot 4.3 to 4.4.dev3 with the fresh-project case, using OmniLight3D shadows with vertex shading on Vulkan Forward+. Investigate the rendering behavior around the reported face-flipped and shadows-only boxes; done means reproducing the regression or explaining why the two project states differ and confirming correct shadows in the affected case.

Written by the indexing model from the issue text.