Gitlab works a bit strangely, Martins. It doesn't use the key from /root/.ssh (for obvious reasons), there's also no user git with a home directory /home/git in which to find a .ssh subdirectory. The key is certainly somewhere to be found (although it's strange that the backup didn't backup the ssh key or the OTP secrets), you're right. I blame it almost being bedtime when I finished it for not thinking to go hunt down exactly where it stored it.
Once we move away from Gitlab, though, I'll make sure we reuse it so that transition can be as smooth as possible.