### 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_READ_THREAD_GUARD_V(false);
	return size_2d_override_stretch;
}
void SubViewport::set_update_mode(UpdateMode p_mode) {
	ERR_MAIN_THREAD_GUARD;
	update_mode = p_mode;
	RS::get_singleton()->viewport_set_update_mode(get_viewport_rid(), RS::ViewportUpdateMode(p_mode));
}
SubViewport::UpdateMode SubViewport::get_update_mode() const {
	ERR_READ_THREAD_GUARD_V(UPDATE_DISABLED);
	return update_mode;
}
void SubViewport::set_clear_mode(ClearMode p_mode) {
	ERR_MAIN_THREAD_GUARD;
	clear_mode = p_mode;
	RS::get_singleton()->viewport_set_clear_mode(get_viewport_rid(), RS::ViewportClearMode(p_mode));
}
SubViewport::ClearMode SubViewport::get_clear_mode() const {
	ERR_READ_THREAD_GUARD_V(CLEAR_MODE_ALWAYS);
	return clear_mode;
}
DisplayServer::WindowID SubViewport::get_window_id() const {
	ERR_READ_THREAD_GUARD_V(DisplayServer::INVALID_WINDOW_ID);
	return DisplayServer::INVALID_WINDOW_ID;
}
Transform2D SubViewport::get_screen_transform_internal(bool p_absolute_position) const {