### 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("_process_picking"), &Viewport::_process_picking);
#ifndef _3D_DISABLED
	ClassDB::bind_method(D_METHOD("set_world_3d", "world_3d"), &Viewport::set_world_3d);
	ClassDB::bind_method(D_METHOD("get_world_3d"), &Viewport::get_world_3d);
	ClassDB::bind_method(D_METHOD("find_world_3d"), &Viewport::find_world_3d);
	ClassDB::bind_method(D_METHOD("set_use_own_world_3d", "enable"), &Viewport::set_use_own_world_3d);
	ClassDB::bind_method(D_METHOD("is_using_own_world_3d"), &Viewport::is_using_own_world_3d);
	ClassDB::bind_method(D_METHOD("get_camera_3d"), &Viewport::get_camera_3d);
	ClassDB::bind_method(D_METHOD("set_as_audio_listener_3d", "enable"), &Viewport::set_as_audio_listener_3d);
	ClassDB::bind_method(D_METHOD("is_audio_listener_3d"), &Viewport::is_audio_listener_3d);
	ClassDB::bind_method(D_METHOD("set_disable_3d", "disable"), &Viewport::set_disable_3d);
	ClassDB::bind_method(D_METHOD("is_3d_disabled"), &Viewport::is_3d_disabled);
	ClassDB::bind_method(D_METHOD("set_use_xr", "use"), &Viewport::set_use_xr);
	ClassDB::bind_method(D_METHOD("is_using_xr"), &Viewport::is_using_xr);
	ClassDB::bind_method(D_METHOD("set_scaling_3d_mode", "scaling_3d_mode"), &Viewport::set_scaling_3d_mode);
	ClassDB::bind_method(D_METHOD("get_scaling_3d_mode"), &Viewport::get_scaling_3d_mode);
	ClassDB::bind_method(D_METHOD("set_scaling_3d_scale", "scale"), &Viewport::set_scaling_3d_scale);
	ClassDB::bind_method(D_METHOD("get_scaling_3d_scale"), &Viewport::get_scaling_3d_scale);
	ClassDB::bind_method(D_METHOD("set_fsr_sharpness", "fsr_sharpness"), &Viewport::set_fsr_sharpness);
	ClassDB::bind_method(D_METHOD("get_fsr_sharpness"), &Viewport::get_fsr_sharpness);
	ClassDB::bind_method(D_METHOD("set_texture_mipmap_bias", "texture_mipmap_bias"), &Viewport::set_texture_mipmap_bias);
	ClassDB::bind_method(D_METHOD("get_texture_mipmap_bias"), &Viewport::get_texture_mipmap_bias);
	ClassDB::bind_method(D_METHOD("set_vrs_mode", "mode"), &Viewport::set_vrs_mode);
	ClassDB::bind_method(D_METHOD("get_vrs_mode"), &Viewport::get_vrs_mode);
	ClassDB::bind_method(D_METHOD("set_vrs_texture", "texture"), &Viewport::set_vrs_texture);
	ClassDB::bind_method(D_METHOD("get_vrs_texture"), &Viewport::get_vrs_texture);
	ADD_PROPERTY(PropertyInfo(Variant::BOOL, "disable_3d"), "set_disable_3d", "is_3d_disabled");
	ADD_PROPERTY(PropertyInfo(Variant::BOOL, "use_xr"), "set_use_xr", "is_using_xr");
	ADD_PROPERTY(PropertyInfo(Variant::BOOL, "own_world_3d"), "set_use_own_world_3d", "is_using_own_world_3d");
	ADD_PROPERTY(PropertyInfo(Variant::OBJECT, "world_3d", PROPERTY_HINT_RESOURCE_TYPE, "World3D"), "set_world_3d", "get_world_3d");