This is a recap of how I seem to have resolved my file sharing issue. Maybe it will be useful to others.
1. Under: General > File Sharing and Media Sharing, I switched both OFF on both iMacs, shut down both machines, restarted both, and turned File Sharing and Media Sharing back on.
2. What follows happened exactly the same on both iMacs:
Under: Media Sharing > under the (i) icon there is the option to turn Home Sharing on. It was on so I turned it off and turned it back on again. This required my Apple ID & Password which I entered. This gave me an endless spinning wheel by the ID. I had to Option-Command-Escape out of System Settings. I went back and tried again and this time it read that Home Sharing has been turned on and the appropriate Family Icon Drive appeared.
3. Under: General > Sharing > Media Sharing > Home Sharing & Share Media with Guests.
Log on to both computers with the same Administrator ID and Password
4. Under: (Your Name) > Family Sharing, select Users who can have access.
Make sure all have Read & Write Permissions.
5. Under: Privacy & Security > Full Disk Access > SMBD is on.
6. Under: Desktop Menu > Go > Connect To Server, I've saved the functioning path to the other device. Example: smb://(other-mac-name)._smb._tcp.local
I have Energy Saver > Wake up for Network Access Off so, I think that's why the other computer has to be awake to access... but I haven't tested that.
Good luck.