Simplify new system deployment reusing `kci-easy`

Staging script currently deploys the new system by [running docker-compose actions](https://github.com/kernelci/kernelci-deploy/blob/main/staging.kernelci.org#L332).

It could be beneficial to align it with how `kci-easy` deployment works when it is adopted as a default development environment. It would help keeping staging instance as close as possible to the environment developers test on locally.

Start with the docker-compose actions in staging.kernelci.org around line 332, then compare them with how kci-easy deployment works. Determine the deployment steps that should be shared so staging stays close to the default development environment. Done means the staging deployment reuses the kci-easy approach rather than its current separate actions.

Written by the indexing model from the issue text.