### 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)

if (co && co->is_inside_tree()) {
				if (p_clean_all_frames && p_paused_only && co->can_process()) {
					continue;
				}
				co->_mouse_shape_exit(E.key.second);
			}
		}
		shapes_to_erase.push_back(E.key);
	}
	while (shapes_to_erase.size()) {
		physics_2d_shape_mouseover.erase(shapes_to_erase.front()->get());
		shapes_to_erase.pop_front();
	}
}
void Viewport::_gui_grab_click_focus(Control *p_control) {
	gui.mouse_click_grabber = p_control;
	call_deferred(SNAME("_post_gui_grab_click_focus"));
}
void Viewport::_post_gui_grab_click_focus() {
	Control *focus_grabber = gui.mouse_click_grabber;
	if (!focus_grabber) {
		
		return;
	}
	gui.mouse_click_grabber = nullptr;
	if (gui.mouse_focus) {
		if (gui.mouse_focus == focus_grabber) {
			return;
		}
		BitField<MouseButtonMask> mask = gui.mouse_focus_mask;