time machine over network not connnecting

When you do a Migration Assistant restore but are using a reformatted hard disk it can mess up the naming UUID and more complicated stuff. Although how that is causing keychain problems I am not sure.

My advice is to simply get a new drive and start over. Do a fresh clean backup and I think it should work.

Post again if you have issues.

Time Machine backs up in a totally different way when it uses network cf locally connected disks.

I have tested doing backups over network to a hard disk plugged into another Mac.. and whilst it worked it was even less reliable than using a Time Capsule. And the fact is Time Machine is simply a lot better at locally connected target disk.

Partly the problem relates to increased security in the later Mac OS. ie El Capo made big changes to security.. which Sierra will also follow.

So let me alter my advice. (Apologies.. but you have asked the right questions which I did not think carefully enough about).

For a network target.

1. Do NOT use a standard Mac OS. If you want to use Server extensions it has a special TM function that will help no end I am guessing.. but admit to having never tried.

2. Even a Time Capsule is not the ideal target. Especially over wireless it corrupts often enough that I fear the day you actually need the backup it will fail. Much better over ethernet.

3. I do use a Synology NAS which has been a big improvement. Supports Time Machine very well.

OR

4. Use a different backup software. Carbon Copy Cloner (CCC) or Chronosync are likely to work a lot better than Time Machine. You can backup to a disk plugged into a Mac running standard OS. It simply needs to be Mac OS extended journaled format.

For local backups.

Time Machine works much better to local target. But then CCC can produce a bootable clone which gives you instant access to your files. So a partitioned drive big enough to do both CCC and TM can be well worth it. TM can still be useful and does a good job of incremental but for rebuilding a computer CCC every time.

I do strongly recommend people do use alternative to TM nowadays. Even if it is only a monthly backup to a local USB disk.

Also, looking in my keychain access, there's two entries that are labeled Kind as 'Time Machine Password' for what appears to be the same path. Should I delete those two entries and try again?

Yes, that would be worthwhile if you wish to continue with the same setup.

It is important to make sure your Sierra computer has full permissions to access the disk on the Mac Mini.. and this might be difficult if you are using older OS on the Mini.

See my thoughts above.