Currently, there is no way to add a tool a menu using the Python Add-In Wizard.
The only workaround to this is to modify the config.xml file and rearrange the layout structure of the toolbar. Click here for more info.
Thank you for your contribution. The Python Add-in interface isn't receiving enhancements based on ArcMap's mature status in the product lifecycle. Future development is going into the Python developer experience in ArcGIS Pro and our other product offerings.
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