### 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)

void set_positional_shadow_atlas_size(int p_size);
	int get_positional_shadow_atlas_size() const;
	void set_positional_shadow_atlas_16_bits(bool p_16_bits);
	bool get_positional_shadow_atlas_16_bits() const;
	void set_positional_shadow_atlas_quadrant_subdiv(int p_quadrant, PositionalShadowAtlasQuadrantSubdiv p_subdiv);
	PositionalShadowAtlasQuadrantSubdiv get_positional_shadow_atlas_quadrant_subdiv(int p_quadrant) const;
	void set_msaa_2d(MSAA p_msaa);
	MSAA get_msaa_2d() const;
	void set_msaa_3d(MSAA p_msaa);
	MSAA get_msaa_3d() const;
	void set_screen_space_aa(ScreenSpaceAA p_screen_space_aa);
	ScreenSpaceAA get_screen_space_aa() const;
	void set_use_taa(bool p_use_taa);
	bool is_using_taa() const;
	void set_scaling_3d_mode(Scaling3DMode p_scaling_3d_mode);
	Scaling3DMode get_scaling_3d_mode() const;
	void set_scaling_3d_scale(float p_scaling_3d_scale);
	float get_scaling_3d_scale() const;
	void set_fsr_sharpness(float p_fsr_sharpness);
	float get_fsr_sharpness() const;
	void set_texture_mipmap_bias(float p_texture_mipmap_bias);
	float get_texture_mipmap_bias() const;
	void set_use_debanding(bool p_use_debanding);
	bool is_using_debanding() const;
	void set_mesh_lod_threshold(float p_pixels);
	float get_mesh_lod_threshold() const;
	void set_use_occlusion_culling(bool p_us_occlusion_culling);
	bool is_using_occlusion_culling() const;
	Vector2 get_camera_coords(const Vector2 &p_viewport_coords) const;
	Vector2 get_camera_rect_size() const;