You could attempt to install the NVMe in your mini PC, if it takes them. Then boot from it and attempt a backup of your database to external storage. It may not work due to the version of Roon OS/Roon Server being optimised for the Nucleus+.
If successful you’d be able to restore your new Roon Server.
There are thumb-drive Linux distributions available. Even the ubuntu install media is able to do just that (choose “try” instead of “install”). With such a (temporary) Linux distribution available you should be able to access the old SSD and copy data to a save place (maybe an[other] thumb drive or external USB disk if the internal Windows disk is encrypted).
We can see an active RoonServer instance on a Windows 11 machine. Did you have a chance to connect the HDMI output of the Nucleus to a monitor? Please let us know what is displayed or share a photo. Thanks!