### 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
Button *tb = memnew(Button);
	tb->set_flat(true);
	tb->connect("toggled", callable_mp(this, &EditorNode::_bottom_panel_switch).bind(bottom_panel_items.size()));
	tb->set_text(p_text);
	tb->set_toggle_mode(true);
	tb->set_focus_mode(Control::FOCUS_NONE);
	bottom_panel_vb->add_child(p_item);
	bottom_panel_hb->move_to_front();
	bottom_panel_hb_editors->add_child(tb);
	p_item->set_v_size_flags(Control::SIZE_EXPAND_FILL);
	p_item->hide();
	BottomPanelItem bpi;
	bpi.button = tb;
	bpi.control = p_item;
	bpi.name = p_text;
	bottom_panel_items.push_back(bpi);
	return tb;
}
void EditorNode::hide_bottom_panel() {