Earlier quoted context omitted.
Am I the only one who finds this conceptually confusing?
Nope, me too. The whole Repo network thing is not User facing at all. It is an internal thing at GitHub to allow easier pull requests between repo's. But it isn't a concept git knows, and it doesn't affect GitHub users at all except for this one weird thing.
There are some user-facing parts: You can find the fork network and some related bits under repo insights. (The UX is not great.)
https://github.com/apache/airflow/forks?include=active&page=...