When a GitHub App is installed into an organization it's more appropriate to get the installation ID using the /orgs/{org}/installations API. Currently we work around this issue by providing a known-existing repository, but are getting closer to situations where we don't (or don't want to) know what repos are available.

Adding an organization input, similar to the current repository input, would provide a better experience for that use case.

I can take some time to submit a PR for this either later this week or next if someone else doesn't beat me to it.