Thanks a lot for submitting the patch, I'm eager to see emacs-next in upstream!
Every Emacs version creates a dir along the lines of .gix-profile/share/emacs/version/lisp. Current emacs from master hardcodes this version to 27.0.50, so this path becomes .gix-profile/share/emacs/27.0.50/lisp. But since we set version based on commit in this submitted patch, EMACSLOADPATH becomes invalid and this specific directory doesn't end up in the guix-profile/etc/profile script, so when you run emacs, you get multiple errors because Emacs can't load builtin packages. I think that hardcoding a version of emacs-next to "27.0.50" should work well. I'm attaching a patch that can be applied to Amin's emacs-next patch.
Regards,
Valentin