### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
ofs.x += s.x * 4;
				ofs.x += s.x;
			} break;
			case DOCK_SLOT_RIGHT_BR: {
				ofs.x += s.x * 4;
				ofs += s;
			} break;
		}
		Rect2 r(ofs, s);
		dock_select_rect[i] = r;
		r.position += Vector2(2, 5);
		r.size -= Vector2(4, 7);
		if (i == dock_select_rect_over_idx) {
			dock_select->draw_rect(r, used_selected);
		} else if (dock_slot[i]->get_tab_count() == 0) {
			dock_select->draw_rect(r, unused);
		} else {
			dock_select->draw_rect(r, used);
		}
		for (int j = 0; j < MIN(3, dock_slot[i]->get_tab_count()); j++) {
			int xofs = (r.size.width / 3) * j;
			Color c = used;
			if (i == dock_popup_selected_idx && (dock_slot[i]->get_current_tab() > 3 || dock_slot[i]->get_current_tab() == j)) {
				c = tab_selected;
			}
			dock_select->draw_rect(Rect2(2 + ofs.x + xofs, ofs.y, r.size.width / 3 - 1, 3), c);
		}
	}
}
void EditorNode::_save_editor_layout() {