### 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;
	
	vrs_mode = p_vrs_mode;
	switch (p_vrs_mode) {
		case VRS_TEXTURE: {
			RS::get_singleton()->viewport_set_vrs_mode(viewport, RS::VIEWPORT_VRS_TEXTURE);
		} break;
		case VRS_XR: {
			RS::get_singleton()->viewport_set_vrs_mode(viewport, RS::VIEWPORT_VRS_XR);
		} break;
		default: {
			RS::get_singleton()->viewport_set_vrs_mode(viewport, RS::VIEWPORT_VRS_DISABLED);
		} break;
	}
	notify_property_list_changed();
}
Viewport::VRSMode Viewport::get_vrs_mode() const {
	ERR_READ_THREAD_GUARD_V(VRS_DISABLED);
	return vrs_mode;
}
void Viewport::set_vrs_texture(Ref<Texture2D> p_texture) {
	ERR_MAIN_THREAD_GUARD;
	vrs_texture = p_texture;
	
	RID tex = p_texture.is_valid() ? p_texture->get_rid() : RID();
	RS::get_singleton()->viewport_set_vrs_texture(viewport, tex);
}
Ref<Texture2D> Viewport::get_vrs_texture() const {