### 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)

ClassDB::bind_method(D_METHOD("get_debug_draw"), &Viewport::get_debug_draw);
	ClassDB::bind_method(D_METHOD("get_render_info", "type", "info"), &Viewport::get_render_info);
	ClassDB::bind_method(D_METHOD("get_texture"), &Viewport::get_texture);
	ClassDB::bind_method(D_METHOD("set_physics_object_picking", "enable"), &Viewport::set_physics_object_picking);
	ClassDB::bind_method(D_METHOD("get_physics_object_picking"), &Viewport::get_physics_object_picking);
	ClassDB::bind_method(D_METHOD("set_physics_object_picking_sort", "enable"), &Viewport::set_physics_object_picking_sort);
	ClassDB::bind_method(D_METHOD("get_physics_object_picking_sort"), &Viewport::get_physics_object_picking_sort);
	ClassDB::bind_method(D_METHOD("get_viewport_rid"), &Viewport::get_viewport_rid);
	ClassDB::bind_method(D_METHOD("push_text_input", "text"), &Viewport::push_text_input);
	ClassDB::bind_method(D_METHOD("push_input", "event", "in_local_coords"), &Viewport::push_input, DEFVAL(false));
#ifndef DISABLE_DEPRECATED
	ClassDB::bind_method(D_METHOD("push_unhandled_input", "event", "in_local_coords"), &Viewport::push_unhandled_input, DEFVAL(false));
#endif 
	ClassDB::bind_method(D_METHOD("get_camera_2d"), &Viewport::get_camera_2d);
	ClassDB::bind_method(D_METHOD("set_as_audio_listener_2d", "enable"), &Viewport::set_as_audio_listener_2d);
	ClassDB::bind_method(D_METHOD("is_audio_listener_2d"), &Viewport::is_audio_listener_2d);
	ClassDB::bind_method(D_METHOD("get_mouse_position"), &Viewport::get_mouse_position);
	ClassDB::bind_method(D_METHOD("warp_mouse", "position"), &Viewport::warp_mouse);
	ClassDB::bind_method(D_METHOD("update_mouse_cursor_state"), &Viewport::update_mouse_cursor_state);
	ClassDB::bind_method(D_METHOD("gui_get_drag_data"), &Viewport::gui_get_drag_data);
	ClassDB::bind_method(D_METHOD("gui_is_dragging"), &Viewport::gui_is_dragging);
	ClassDB::bind_method(D_METHOD("gui_is_drag_successful"), &Viewport::gui_is_drag_successful);
	ClassDB::bind_method(D_METHOD("gui_release_focus"), &Viewport::gui_release_focus);
	ClassDB::bind_method(D_METHOD("gui_get_focus_owner"), &Viewport::gui_get_focus_owner);
	ClassDB::bind_method(D_METHOD("set_disable_input", "disable"), &Viewport::set_disable_input);
	ClassDB::bind_method(D_METHOD("is_input_disabled"), &Viewport::is_input_disabled);
	ClassDB::bind_method(D_METHOD("_gui_remove_focus_for_window"), &Viewport::_gui_remove_focus_for_window);
	ClassDB::bind_method(D_METHOD("_post_gui_grab_click_focus"), &Viewport::_post_gui_grab_click_focus);
	ClassDB::bind_method(D_METHOD("set_positional_shadow_atlas_size", "size"), &Viewport::set_positional_shadow_atlas_size);
	ClassDB::bind_method(D_METHOD("get_positional_shadow_atlas_size"), &Viewport::get_positional_shadow_atlas_size);