### 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)

StringName shortcut_input_group;
	StringName unhandled_input_group;
	StringName unhandled_key_input_group;
	void _update_audio_listener_2d();
	bool disable_3d = false;
	void _propagate_viewport_notification(Node *p_node, int p_what);
	void _update_global_transform();
	RID texture_rid;
	DebugDraw debug_draw = DEBUG_DRAW_DISABLED;
	int positional_shadow_atlas_size = 2048;
	bool positional_shadow_atlas_16_bits = true;
	PositionalShadowAtlasQuadrantSubdiv positional_shadow_atlas_quadrant_subdiv[4];
	MSAA msaa_2d = MSAA_DISABLED;
	MSAA msaa_3d = MSAA_DISABLED;
	ScreenSpaceAA screen_space_aa = SCREEN_SPACE_AA_DISABLED;
	bool use_taa = false;
	Scaling3DMode scaling_3d_mode = SCALING_3D_MODE_BILINEAR;
	float scaling_3d_scale = 1.0;
	float fsr_sharpness = 0.2f;
	float texture_mipmap_bias = 0.0f;
	bool use_debanding = false;
	float mesh_lod_threshold = 1.0;
	bool use_occlusion_culling = false;
	Ref<ViewportTexture> default_texture;
	HashSet<ViewportTexture *> viewport_textures;
	void _update_viewport_path();
	SDFOversize sdf_oversize = SDF_OVERSIZE_120_PERCENT;
	SDFScale sdf_scale = SDF_SCALE_50_PERCENT;
	uint32_t canvas_cull_mask = 0xffffffff; 
	enum SubWindowDrag {