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Is the drive encrypted? If so, then that might be the issue. I haven’t tried with VirtualBox, but with VMWare Fusion, I occasionally have issues where the password prompt doesn’t display when I attempt to mount the drive.
Have you tried manually forcing an AFP connection? In Finder on your old Mac, from the "Go" menu, choose "Connect to Server". In the sever address field specify the afp protocol and the IP address of your Mac with the shared folder (e.g. "afp://192.168.0.12"). Note, if you are not sharing the whole drive then you might have to specify the full path to the folder you are sharing.
Then you might need to add the drive to the ‘Shared Folders’ section of the ‘Sharing’ panel. But first, I would just try turning file sharing off, waiting 10 seconds, and turning it back on.
Most likely you will be better off using a dedicated sync app like ChronoSync, rather than trying to coerce Time Machine into doing something that it was not designed for. This is especially true if you plan on syncing these systems often.
You might want to check to make sure that both file systems are set to use the same level of case-sensitivity (i.e. both are case-sensitive, or both are case-insensitive).
My guess is that in the Wifi section the values shown are the average throughput for the entire range of the graph shown. And in the Processes section the values shown are the current throughput for each process.
If you are using iOS 13, then you have to use Catalina (or later) if you want to sync Reminders. Dumb but true. Since I’m still using Mojave, this is the main reason I haven’t updated to iOS 13.
My guess is, that with Filevault enabled, all new users get automatically added to its “enabled” list. If so, then you could try adding the new user (with a password), going to System Preferences->Security & Preferences->Filevault and removing the new user from the “Enabled Users” list. Then login as the new user and change their password to be empty.
Do you have Filevault enabled? If so, it may be requiring a password if it is trying to automatically add the new user to the list of users authorized to unlock the disk.
ChronoSync can be configured to trigger the sync immediately after both drives have mounted. It also has the ability to make a mirror sync, and to only sync the files that have changed. In my opinion, out of all the apps that have been suggested so far, it is the best one to do what you wish.