Switch nighly builds workflow to use `packit`

[kontura]

The nightly builds workflow should be the last thing that actively uses rpm-gitoverlay: https://github.com/rpm-software-management/ci-dnf-stack/blob/main/.github/workflows/nightly.yml#L40

I think we should switch it to use packit like the rest of our CI if possible.

rpm-gitoverlay will require more maintenance in f43 due to breaking changes in its dependencies.
We should also clean up old overlays.