"None of our shares have vested" seems to imply they both hold options, with the other founder holding a majority of the issued options.

Yes this is correct - apologize if I wasn't clear with this. From what I understand and my previous experiences at startups it was a standard vesting structure where ownership vests over 4-years with a 1-year cliff (or at an acquisition event). On day-1 neither I nor my co-founder had any shares vested.