### 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)

BIND_ENUM_CONSTANT(SDF_OVERSIZE_MAX);
	BIND_ENUM_CONSTANT(SDF_SCALE_100_PERCENT);
	BIND_ENUM_CONSTANT(SDF_SCALE_50_PERCENT);
	BIND_ENUM_CONSTANT(SDF_SCALE_25_PERCENT);
	BIND_ENUM_CONSTANT(SDF_SCALE_MAX);
	BIND_ENUM_CONSTANT(VRS_DISABLED);
	BIND_ENUM_CONSTANT(VRS_TEXTURE);
	BIND_ENUM_CONSTANT(VRS_XR);
	BIND_ENUM_CONSTANT(VRS_MAX);
}
void Viewport::_validate_property(PropertyInfo &p_property) const {
	if (vrs_mode != VRS_TEXTURE && (p_property.name == "vrs_texture")) {
		p_property.usage = PROPERTY_USAGE_NO_EDITOR;
	}
}
Viewport::Viewport() {
	world_2d = Ref<World2D>(memnew(World2D));
	world_2d->register_viewport(this);
	viewport = RenderingServer::get_singleton()->viewport_create();
	texture_rid = RenderingServer::get_singleton()->viewport_get_texture(viewport);
	default_texture.instantiate();
	default_texture->vp = const_cast<Viewport *>(this);
	viewport_textures.insert(default_texture.ptr());
	default_texture->proxy = RS::get_singleton()->texture_proxy_create(texture_rid);
	canvas_layers.insert(nullptr); // This eases picking code (interpreted as the canvas of the Viewport).
	set_positional_shadow_atlas_size(positional_shadow_atlas_size);
	for (int i = 0; i < 4; i++) {
		positional_shadow_atlas_quadrant_subdiv[i] = SHADOW_ATLAS_QUADRANT_SUBDIV_MAX;
	}
	set_positional_shadow_atlas_quadrant_subdiv(0, SHADOW_ATLAS_QUADRANT_SUBDIV_4);