### 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("set_positional_shadow_atlas_16_bits", "enable"), &Viewport::set_positional_shadow_atlas_16_bits);
	ClassDB::bind_method(D_METHOD("get_positional_shadow_atlas_16_bits"), &Viewport::get_positional_shadow_atlas_16_bits);
	ClassDB::bind_method(D_METHOD("set_snap_controls_to_pixels", "enabled"), &Viewport::set_snap_controls_to_pixels);
	ClassDB::bind_method(D_METHOD("is_snap_controls_to_pixels_enabled"), &Viewport::is_snap_controls_to_pixels_enabled);
	ClassDB::bind_method(D_METHOD("set_snap_2d_transforms_to_pixel", "enabled"), &Viewport::set_snap_2d_transforms_to_pixel);
	ClassDB::bind_method(D_METHOD("is_snap_2d_transforms_to_pixel_enabled"), &Viewport::is_snap_2d_transforms_to_pixel_enabled);
	ClassDB::bind_method(D_METHOD("set_snap_2d_vertices_to_pixel", "enabled"), &Viewport::set_snap_2d_vertices_to_pixel);
	ClassDB::bind_method(D_METHOD("is_snap_2d_vertices_to_pixel_enabled"), &Viewport::is_snap_2d_vertices_to_pixel_enabled);
	ClassDB::bind_method(D_METHOD("set_positional_shadow_atlas_quadrant_subdiv", "quadrant", "subdiv"), &Viewport::set_positional_shadow_atlas_quadrant_subdiv);
	ClassDB::bind_method(D_METHOD("get_positional_shadow_atlas_quadrant_subdiv", "quadrant"), &Viewport::get_positional_shadow_atlas_quadrant_subdiv);
	ClassDB::bind_method(D_METHOD("set_input_as_handled"), &Viewport::set_input_as_handled);
	ClassDB::bind_method(D_METHOD("is_input_handled"), &Viewport::is_input_handled);
	ClassDB::bind_method(D_METHOD("set_handle_input_locally", "enable"), &Viewport::set_handle_input_locally);
	ClassDB::bind_method(D_METHOD("is_handling_input_locally"), &Viewport::is_handling_input_locally);
	ClassDB::bind_method(D_METHOD("set_default_canvas_item_texture_filter", "mode"), &Viewport::set_default_canvas_item_texture_filter);
	ClassDB::bind_method(D_METHOD("get_default_canvas_item_texture_filter"), &Viewport::get_default_canvas_item_texture_filter);
	ClassDB::bind_method(D_METHOD("set_embedding_subwindows", "enable"), &Viewport::set_embedding_subwindows);
	ClassDB::bind_method(D_METHOD("is_embedding_subwindows"), &Viewport::is_embedding_subwindows);
	ClassDB::bind_method(D_METHOD("set_canvas_cull_mask", "mask"), &Viewport::set_canvas_cull_mask);
	ClassDB::bind_method(D_METHOD("get_canvas_cull_mask"), &Viewport::get_canvas_cull_mask);
	ClassDB::bind_method(D_METHOD("set_canvas_cull_mask_bit", "layer", "enable"), &Viewport::set_canvas_cull_mask_bit);
	ClassDB::bind_method(D_METHOD("get_canvas_cull_mask_bit", "layer"), &Viewport::get_canvas_cull_mask_bit);
	ClassDB::bind_method(D_METHOD("set_default_canvas_item_texture_repeat", "mode"), &Viewport::set_default_canvas_item_texture_repeat);
	ClassDB::bind_method(D_METHOD("get_default_canvas_item_texture_repeat"), &Viewport::get_default_canvas_item_texture_repeat);
	ClassDB::bind_method(D_METHOD("set_sdf_oversize", "oversize"), &Viewport::set_sdf_oversize);
	ClassDB::bind_method(D_METHOD("get_sdf_oversize"), &Viewport::get_sdf_oversize);
	ClassDB::bind_method(D_METHOD("set_sdf_scale", "scale"), &Viewport::set_sdf_scale);
	ClassDB::bind_method(D_METHOD("get_sdf_scale"), &Viewport::get_sdf_scale);
	ClassDB::bind_method(D_METHOD("set_mesh_lod_threshold", "pixels"), &Viewport::set_mesh_lod_threshold);
	ClassDB::bind_method(D_METHOD("get_mesh_lod_threshold"), &Viewport::get_mesh_lod_threshold);