### Godot version

v4.1.dev.custom_build [18112ba36]

### System information

Linux Mint 21.1, NVIDIA GeForce GTX 1050 Ti,  Vulkan API 1.3.205

### Issue description

This is a regression from #64388. 

Textures seem to be used differently in 2D and 3D. They are rendered using the `RID` in 3D, and changing the `viewport_path` will cause the `RID` to change.

https://github.com/godotengine/godot/assets/30386067/ad393fe8-50c1-4a89-870d-58d4e224bcc6


### Steps to reproduce

1. Download and import MRP.
2. Open 1.tscn, and try to switch the `viewport_path` of the `MeshInstance3D:mesh:material:albedo_texture` in the MeshInstance3D node.
3. After switching, the MeshInstance3D is rendered as white in the editor;
4. Close and then reopen 1.tscn.

### Minimal reproduction project

[ViewportTexture-change-viewport_path.zip](https://github.com/godotengine/godot/files/11509010/ViewportTexture-change-viewport_path.zip)

ERR_MAIN_THREAD_GUARD;
	
	
	
	scaling_3d_scale = CLAMP(p_scaling_3d_scale, 0.1, 2.0);
	RS::get_singleton()->viewport_set_scaling_3d_scale(viewport, scaling_3d_scale);
}
float Viewport::get_scaling_3d_scale() const {
	ERR_READ_THREAD_GUARD_V(0);
	return scaling_3d_scale;
}
void Viewport::set_fsr_sharpness(float p_fsr_sharpness) {
	ERR_MAIN_THREAD_GUARD;
	if (fsr_sharpness == p_fsr_sharpness) {
		return;
	}
	if (p_fsr_sharpness < 0.0f) {
		p_fsr_sharpness = 0.0f;
	}
	fsr_sharpness = p_fsr_sharpness;
	RS::get_singleton()->viewport_set_fsr_sharpness(viewport, p_fsr_sharpness);
}
float Viewport::get_fsr_sharpness() const {
	ERR_READ_THREAD_GUARD_V(0);
	return fsr_sharpness;
}
void Viewport::set_texture_mipmap_bias(float p_texture_mipmap_bias) {