Pixel artifacts on model in 3D - Gets more prevalent the lower the resolution

### Tested versions

- Tested in 4.2.2.stable

### System information

MacOS 14.4.1 - M1 Pro - Vulkan (Forward+) / Windows 11 23H2 - GTX 1060 6GB

### Issue description

Pixel artifacts appear on the player character model in the 3D scene. The rogue pixels appear to be behaving with an "X-ray" effect, where it shows color of the geometry behind what should be rendered in front.

Notice how the artifacts become much more frequent and noticeable the lower resolution the game is set at. Videos of tested resolutions are as follows:

https://github.com/godotengine/godot/assets/65742713/c16ec3e8-9962-4426-963a-aa463621df21

https://github.com/godotengine/godot/assets/65742713/5098d100-6ae2-45f1-965a-6b11c9a5d48f

https://github.com/godotengine/godot/assets/65742713/0b9316a7-cc60-44b7-a942-821757c5695d

https://github.com/godotengine/godot/assets/65742713/f5619b1f-cbcb-4e30-ad02-ca270bd1034c

### Steps to reproduce

1. Open the attached MRP and run the game.
2. Walk around with A/D and jump with Space.
3. Observe artifacts as the player model animates.
4. Experiment with the resolution in Project > Project Settings > Window > Size.

I worked with the Godot Discord community to troubleshoot for a few days, including ensuring model LODs were turned off, changing rendering and AA settings, but nothing fixed the issue.

### Minimal reproduction project (MRP)

[Pixel Artifacts.zip](https://github.com/godotengine/godot/files/15214415/Pixel.Artifacts.zip)

Open the attached Pixel Artifacts.zip minimal reproduction project and run it with the reported Vulkan Forward+ settings. Reproduce the player-model artifacts while changing Project > Project Settings > Window > Size, then inspect the relevant 3D rendering path. Done means the rogue pixels no longer appear across the reported resolutions and systems.

Written by the indexing model from the issue text.