Some organisations require applications to request access before allowing access to any data (including notifications) about their repositories.
To check if Gitify is approved by your organisation you can go to settings, then click on Gitify and scroll to Organization access.

You can debug Gitify by pressing alt + command + I. This will open the dev tools and then you can see any logs, network requests etc.

You can contribute to Gitify by opening a pull request @ gitify-app/gitify

This is part of the permissions/entitlements when using the Play sound system setting.