Sadly, creating a new Organisation on the Gogs Server via the REST API doesn't appear to be possible: #8 (comment) so the next best thing is to:
a) create the org that we need manually via the Web UI: https://gogs-server.fly.dev/org/create
b) list all the orgs we have access to via REST API e.g: GET /user/orgs
c) if the org we need already exists, then we create the repo in that org.
otherwise we create the repo in the "global" org but name-space it to the desired org.
This isn't ideal, obviously, but I think it might be better than nothing. 💭