### 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)

mm->set_position(pos);
			Control::CursorShape cursor_shape = Control::CURSOR_ARROW;
			{
				Control *c = over;
				Vector2 cpos = pos;
				while (c) {
					if (!gui.mouse_focus_mask.is_empty() || c->has_point(cpos)) {
						cursor_shape = c->get_cursor_shape(cpos);
					} else {
						cursor_shape = Control::CURSOR_ARROW;
					}
					cpos = c->get_transform().xform(cpos);
					if (cursor_shape != Control::CURSOR_ARROW) {
						break;
					}
					if (c->data.mouse_filter == Control::MOUSE_FILTER_STOP) {
						break;
					}
					if (c->is_set_as_top_level()) {
						break;
					}
					c = c->get_parent_control();
				}
			}
			ds_cursor_shape = (DisplayServer::CursorShape)cursor_shape;
			bool stopped = over->can_process() && _gui_call_input(over, mm);
			if (stopped) {
				set_input_as_handled();
			}
		}