### 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
dock_slot[nrect]->show();
			dock_select->queue_redraw();
			_update_dock_slots_visibility(true);
			_edit_current();
			_save_editor_layout();
		}
	}
}
void EditorNode::_dock_popup_exit() {
	dock_select_rect_over_idx = -1;
	dock_select->queue_redraw();
}
void EditorNode::_dock_pre_popup(int p_which) {
	dock_popup_selected_idx = p_which;
}
void EditorNode::_dock_move_left() {
	if (dock_popup_selected_idx < 0 || dock_popup_selected_idx >= DOCK_SLOT_MAX) {
		return;
	}
	Control *current_ctl = dock_slot[dock_popup_selected_idx]->get_tab_control(dock_slot[dock_popup_selected_idx]->get_current_tab());
	Control *prev_ctl = dock_slot[dock_popup_selected_idx]->get_tab_control(dock_slot[dock_popup_selected_idx]->get_current_tab() - 1);
	if (!current_ctl || !prev_ctl) {
		return;
	}
	dock_slot[dock_popup_selected_idx]->move_child(current_ctl, prev_ctl->get_index(false));
	dock_select->queue_redraw();
	_edit_current();
	_save_editor_layout();
}
void EditorNode::_dock_move_right() {