According to the code, :menu doesn't support setting an icon for touchbar submenus.

For example in the hypothetical nested menu TouchBar.Example.Thing, TouchBar.Example can only be plain a plain text (or emoji) button, but TouchBar.Example.Thing could have an icon declared in the :menu command that defined it.

The (semi) original touchbar implementation (#715) suggests using the macmenu command to support extra customization options.