In the old Windows start menu you could Customize and Add a new entry to the Programs menu. With Classic Shell there is no visible way to do that - none of the many tabs in the configuration dialogue box have an Add button. Not even Customize Start Menu lets you add a new entry that's not already in the list.
It is possible by right-clicking, but that can be difficult on a touchscreen device. In any case a visible button would be more discoverable than a right-click menu. Please make an Add button in a fairly obvious place that lets you add new programs to the start menu. That is surely the most common customization people do.