Wow.. Xserve.. part of the ancient world.
Apple opted out of the server world pretty much completely. All the money is in iPhones.
Synology NAS is the way to go.. You could even buy a rack mount unit if that is the best fit.
QNAP is also popular but Synology is certainly easiest to get working. It does a very good job of reliable backups with Time Machine.
I am not sure what you mean by software.
Time Machine is not as reliable as it used to be, especially when backing up to network clients. Apple made some serious changes to TM at Catalina with no explanation. We are all struggling with the issues it introduced.
The main point is don't trust Time Machine alone. I have a local backup of the computer to a USB drive using Carbon Copy Cloner. This is bootable clone. CCC have moved ahead and can reproduce APFS boot and data whereas Time Machine is still going to require HFS+ formatted disks. I strongly recommend you create a clone of the laptops. I would buy a self powered USB drive for each laptop at least (cheap and 1-2TB more than large enough) and perhaps a larger desktop USB for any desktop Mac. Larger 3.5" disks are more reliable and faster. But you can share a larger disk with a few different computers using partitioning.. have not done it personally. CCC KB has the info on what to do. Obviously you need to rotate this disk around the computers.. which makes it less than auto.
Bootable clone makes testing of the backup a cinch. You boot from it.. so in a couple of min you can see if the backup is working and correct. Time Machine is known for holes in the backup or being partially or entirely non-functional because testing the backup is too hard.
