Please provide a relevant screenshot of the specific area where and how you are trying to add a menu to the page with the URL of the page to check it myself and help you out accordingly.
This header is made on the basis of elementor pro while I’m waiting for a solution to make the woodmart one work, because some woodmart menus interest me, especially the login/registration one, which I can’t take over with elementor.
Please disable the elementor header and footer if you are using and then try adding the header from
Woodmart >> Header Builder. Then Clear cache and check back.
If the problem continues then deactivate all the third-party plugins, activate the parent theme, and provide with the admin panel login details with the permission to debug then we will troubleshoot with the theme plugins.