### 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
Control *current_ctl = dock_slot[dock_popup_selected_idx]->get_tab_control(dock_slot[dock_popup_selected_idx]->get_current_tab());
	Control *next_ctl = dock_slot[dock_popup_selected_idx]->get_tab_control(dock_slot[dock_popup_selected_idx]->get_current_tab() + 1);
	if (!current_ctl || !next_ctl) {
		return;
	}
	dock_slot[dock_popup_selected_idx]->move_child(next_ctl, current_ctl->get_index(false));
	dock_select->queue_redraw();
	_edit_current();
	_save_editor_layout();
}
void EditorNode::_dock_select_draw() {
	Size2 s = dock_select->get_size();
	s.y /= 2.0;
	s.x /= 6.0;
	Color used = Color(0.6, 0.6, 0.6, 0.8);
	Color used_selected = Color(0.8, 0.8, 0.8, 0.8);
	Color tab_selected = theme->get_color(SNAME("mono_color"), EditorStringName(Editor));
	Color unused = used;
	unused.a = 0.4;
	Color unusable = unused;
	unusable.a = 0.1;
	Rect2 unr(s.x * 2, 0, s.x * 2, s.y * 2);
	unr.position += Vector2(2, 5);