if your old macPro 2006 is still working, you can already access all those files using Mac File Sharing.
Set up file sharing on Mac - Apple Support
MacPro drive bays provide a SATA interface, and any enclosure with SATA interfaces for the drives should do the job.
I use an old MacPro (BUT -- Must be running at least 10.13 High Sierra) as a Backup Server. Most Macs in the house send their Time Machine backups there automatically.
OWC/Macsales sells a 4-drive enclosure for SATA drives. I bought one and loaded it with older drives to store backups. You can organize it however you like. Mine is set up as one big logical drive implemented on several different individual drives. JBOD RAID -- "Just a Bunch of Drives" (pasted together into one).