I also posted this question on the official Microsoft Support Community forum, and received this reply from a Microsoft Community Technical Support Specialist.

I understand that you had problems with Outlook groups, you can't add members to the group. In fact, this has been going on for a week or more.

I received feedback from users about this error two months ago, and so far this has been a very difficult problem, and the engineers still haven't finished fixing the error.
If I receive any news, I'll get back to you as soon as I can!

In other words, we don't know why this is happening, and we can't fix it.