### 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
unr.size -= Vector2(4, 7);
	dock_select->draw_rect(unr, unusable);
	dock_tab_move_left->set_disabled(true);
	dock_tab_move_right->set_disabled(true);
	if (dock_popup_selected_idx != -1 && dock_slot[dock_popup_selected_idx]->get_tab_count()) {
		dock_tab_move_left->set_disabled(dock_slot[dock_popup_selected_idx]->get_current_tab() == 0);
		dock_tab_move_right->set_disabled(dock_slot[dock_popup_selected_idx]->get_current_tab() >= dock_slot[dock_popup_selected_idx]->get_tab_count() - 1);
	}
	for (int i = 0; i < DOCK_SLOT_MAX; i++) {
		Vector2 ofs;
		switch (i) {
			case DOCK_SLOT_LEFT_UL: {
			} break;
			case DOCK_SLOT_LEFT_BL: {
				ofs.y += s.y;
			} break;
			case DOCK_SLOT_LEFT_UR: {
				ofs.x += s.x;
			} break;
			case DOCK_SLOT_LEFT_BR: {
				ofs += s;
			} break;
			case DOCK_SLOT_RIGHT_UL: {
				ofs.x += s.x * 4;
			} break;
			case DOCK_SLOT_RIGHT_BL: {
				ofs.x += s.x * 4;
				ofs.y += s.y;
			} break;
			case DOCK_SLOT_RIGHT_UR: {