### 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)

}
	Ref<InputEventMouse> me = ev;
	if (me.is_valid()) {
		gui.last_mouse_pos = me->get_position();
	}
	if (is_embedding_subwindows() && _sub_windows_forward_input(ev)) {
		set_input_as_handled();
		return;
	}
	if (!_can_consume_input_events()) {
		return;
	}
	if (!is_input_handled()) {
		ERR_FAIL_COND(!is_inside_tree());
		get_tree()->_call_input_pause(input_group, SceneTree::CALL_INPUT_TYPE_INPUT, ev, this); 
	}
	if (!is_input_handled()) {
		ERR_FAIL_COND(!is_inside_tree());
		_gui_input_event(ev);
	} else {
		
		_gui_cleanup_internal_state(ev);
	}
	if (!is_input_handled()) {
		_push_unhandled_input_internal(ev);
	}
	event_count++;
}
#ifndef DISABLE_DEPRECATED
void Viewport::push_unhandled_input(const Ref<InputEvent> &p_event, bool p_local_coords) {