I had a site that was not showing the FA icons in the menu though I had success in my own site.
I followed the instructions at https://generatepress.com/forums/topic/fontawesome/ and could see the code in the html.
I found that the link rel for font awesome was not there.
After a lot of head scratching and dead ends I looked at what plugins were different between the sites.
The first one I deactivated resolved the issue!
Conclusion: NextGen Optimiser (an extra for gallery) is incompatible with GP or Font Awesome.