### 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 (mm.is_valid()) {
			if (gui.subwindow_drag == SUB_WINDOW_DRAG_MOVE) {
				Vector2 diff = mm->get_position() - gui.subwindow_drag_from;
				Rect2i new_rect(gui.subwindow_drag_pos + diff, gui.currently_dragged_subwindow->get_size());
				if (gui.currently_dragged_subwindow->is_clamped_to_embedder()) {
					new_rect = gui.currently_dragged_subwindow->fit_rect_in_parent(new_rect, get_visible_rect());
				}
				gui.currently_dragged_subwindow->_rect_changed_callback(new_rect);
				if (DisplayServer::get_singleton()->has_feature(DisplayServer::FEATURE_CURSOR_SHAPE)) {
					DisplayServer::get_singleton()->cursor_set_shape(DisplayServer::CURSOR_MOVE);
				}
			}
			if (gui.subwindow_drag == SUB_WINDOW_DRAG_CLOSE) {
				gui.subwindow_drag_close_inside = gui.subwindow_drag_close_rect.has_point(mm->get_position());
			}
			if (gui.subwindow_drag == SUB_WINDOW_DRAG_RESIZE) {
				Vector2i diff = mm->get_position() - gui.subwindow_drag_from;
				Size2i min_size = gui.currently_dragged_subwindow->get_min_size();
				Size2i min_size_clamped = gui.currently_dragged_subwindow->get_clamped_minimum_size();
				min_size_clamped.x = MAX(min_size_clamped.x, 1);
				min_size_clamped.y = MAX(min_size_clamped.y, 1);
				Rect2i r = gui.subwindow_resize_from_rect;
				Size2i limit = r.size - min_size_clamped;
				switch (gui.subwindow_resize_mode) {
					case SUB_WINDOW_RESIZE_TOP_LEFT: {
						diff.x = MIN(diff.x, limit.x);
						diff.y = MIN(diff.y, limit.y);
						r.position += diff;
						r.size -= diff;
					} break;