A560 was an arcnet card, not ethernet. The usage was the typical things, sharing filesystems, printers etc. The software was early versions of Envoy I guess, or the TCP/IP-stack AS225. There was also the A2060 card for zorro machines.
A2065 was the ethernet equivalent, and is still quite commonly in use. I've never heard of an A565, sadly - it would be quite high on my wish list :-)