If you could link to your repo or a reproduction repo of your problem then it would let me help your scenario. I wasn’t going to tackle all features of Next.js, serverless build and static assets, but might do so if the setup isn’t too involved.
It is indeed out of date. If you track my blog or my examples repo https://github.com/jthegedus/firebase-gcp-examples then you should receive a Next.js update fairly soon. I will address the serverless building of Next.js in a follow up to the updated version of this post.
It may be possible. I have not tried it myself and highly recommend calling https over http endpoints. Just make sure when making calls outside of Google’s environments that you must be on the Firebase Blaze plan — https://stackoverflow.com/a/50007666/7911479
I could not get this to work on Medium. If you got it to work with a published post on Medium could you please share a link? Thanks for sharing the idea regardless!