Why were some of my contacts automatically merged without notice?
I found a solution that kind of works, but IMO it's still unsatisfying.
After some googling, I found that this is a known bug in Android.

Apparently it's fixed (the issue is closed), but I don't think so, because not only do I have these problems now, there are also comments with complaints which were posted after the date when the issue was closed.

One of the comments had a solution that works for me, but it's not ideal:

When I edit the contact (which has my father's name, as mentioned in the question) it shows both contacts to edit...still on the same screen, but clearly separated as different contacts.

On this screen, I can separate or merge them in the options menu. When I choose to separate them, they become two different contacts again...but only on this device. I have to repeat that on the other device in order to separate them there as well.