No javascript errors, that’s strange. Nothing is changing in the DOM when the menu toggle is clicked, which is extra strange.
Is there another cookie/GDPR you can test? We’re not doing anything special – it’s just plain vanilla javascript, so if that plugin is causing it to break, chances are it will break other javascript on your site as you build it.
Ok so I fixed it by accident – after deactivating and reinstalling the plugins multiple times. No idea why it works now – all the plugins are the same.