### 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)

ERR_READ_THREAD_GUARD_V(DEFAULT_CANVAS_ITEM_TEXTURE_FILTER_NEAREST);
	return default_canvas_item_texture_filter;
}
void Viewport::set_default_canvas_item_texture_repeat(DefaultCanvasItemTextureRepeat p_repeat) {
	ERR_MAIN_THREAD_GUARD;
	ERR_FAIL_INDEX(p_repeat, DEFAULT_CANVAS_ITEM_TEXTURE_REPEAT_MAX);
	if (default_canvas_item_texture_repeat == p_repeat) {
		return;
	}
	default_canvas_item_texture_repeat = p_repeat;
	switch (default_canvas_item_texture_repeat) {
		case DEFAULT_CANVAS_ITEM_TEXTURE_REPEAT_DISABLED:
			RS::get_singleton()->viewport_set_default_canvas_item_texture_repeat(viewport, RS::CANVAS_ITEM_TEXTURE_REPEAT_DISABLED);
			break;
		case DEFAULT_CANVAS_ITEM_TEXTURE_REPEAT_ENABLED:
			RS::get_singleton()->viewport_set_default_canvas_item_texture_repeat(viewport, RS::CANVAS_ITEM_TEXTURE_REPEAT_ENABLED);
			break;
		case DEFAULT_CANVAS_ITEM_TEXTURE_REPEAT_MIRROR:
			RS::get_singleton()->viewport_set_default_canvas_item_texture_repeat(viewport, RS::CANVAS_ITEM_TEXTURE_REPEAT_MIRROR);
			break;
		default: {
		}
	}
}
Viewport::DefaultCanvasItemTextureRepeat Viewport::get_default_canvas_item_texture_repeat() const {
	ERR_READ_THREAD_GUARD_V(DEFAULT_CANVAS_ITEM_TEXTURE_REPEAT_DISABLED);
	return default_canvas_item_texture_repeat;
}
void Viewport::set_vrs_mode(Viewport::VRSMode p_vrs_mode) {