Repository Create/Update/Delete Hooks

Is it possible to inject custom code on repository creation, update and removal?

I’d love having Gitea running in a PostgreSQL environment and automatically setup and maintaining git_fdw for each repository, so we can query statistical data for the hosted repos.

Well, there are already organization-wide webhooks you can add, which feature creating, deleting or committing to a repository. Don’t know if that suits your need. You can find them in Org settings -> Webhooks on the left sidebar.