### 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)

SUBWINDOW_CANVAS_LAYER = 1024
	};
	enum VRSMode {
		VRS_DISABLED,
		VRS_TEXTURE,
		VRS_XR,
		VRS_MAX
	};
private:
	friend class ViewportTexture;
	Viewport *parent = nullptr;
	Viewport *gui_parent = nullptr; 
	AudioListener2D *audio_listener_2d = nullptr;
	Camera2D *camera_2d = nullptr;
	HashSet<CanvasLayer *> canvas_layers;
	RID viewport;
	RID current_canvas;
	RID subwindow_canvas;
	bool is_audio_listener_2d_enabled = false;
	RID internal_audio_listener_2d;
	bool override_canvas_transform = false;
	Transform2D canvas_transform_override;
	Transform2D canvas_transform;
	Transform2D global_canvas_transform;
	Transform2D stretch_transform;
	Size2i size = Size2i(512, 512);