Reinstalling macOS from the recovery servers seems to be a major problem for a lot of folks of late.
That's why I suggested using the Command-R startup keys instead of Option-Command-R or Option-Shift-Command-R. The first key combo relies on the local recovery partition hidden on the internal drive. The last two combinations require the bulk of the recovery software to be delivered by Apple servers, which have been flaky at best.
Using the Command-R recovery key combination will allow you to reinstall the latest macOS that was installed on your system, or to use the other apps in macOS Recovery, like Disk Utility.
If you had created a Time Machine backup you could restore your Mac from that.
At this point, if you cannot get a connection to the servers, then you'll need to create a bootable installer somehow. Creating a bootable instaler will require another Mac that can run one of the macOS versions that this old mini can run. If you have access to another Mac built between 2011 and 2017 you can get this done. Create a bootable installer for macOS - Apple Support
The catch here is that you still will need to contact the Apple servers to download the macOS installer app required to create the installer drive. 😕