### 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(0);
	return RS::get_singleton()->viewport_get_render_info(viewport, RS::ViewportRenderInfoType(p_type), RS::ViewportRenderInfo(p_info));
}
void Viewport::set_snap_controls_to_pixels(bool p_enable) {
	ERR_MAIN_THREAD_GUARD;
	snap_controls_to_pixels = p_enable;
}
bool Viewport::is_snap_controls_to_pixels_enabled() const {
	ERR_READ_THREAD_GUARD_V(false);
	return snap_controls_to_pixels;
}
void Viewport::set_snap_2d_transforms_to_pixel(bool p_enable) {
	ERR_MAIN_THREAD_GUARD;
	snap_2d_transforms_to_pixel = p_enable;
	RS::get_singleton()->viewport_set_snap_2d_transforms_to_pixel(viewport, snap_2d_transforms_to_pixel);
}
bool Viewport::is_snap_2d_transforms_to_pixel_enabled() const {
	ERR_READ_THREAD_GUARD_V(false);
	return snap_2d_transforms_to_pixel;
}
void Viewport::set_snap_2d_vertices_to_pixel(bool p_enable) {
	ERR_MAIN_THREAD_GUARD;
	snap_2d_vertices_to_pixel = p_enable;
	RS::get_singleton()->viewport_set_snap_2d_vertices_to_pixel(viewport, snap_2d_vertices_to_pixel);
}
bool Viewport::is_snap_2d_vertices_to_pixel_enabled() const {
	ERR_READ_THREAD_GUARD_V(false);
	return snap_2d_vertices_to_pixel;
}
bool Viewport::gui_is_dragging() const {