I am unable to add a new member on Family Sharing

What is Family Sharing? - What is Family Sharing? - Apple Support - "With Family Sharing, you and up to five other family members can share access to amazing Apple services..."

I am not following how many you actually have in the family already. Six, including yourself, already? If six, somebody has to leave before you can add another.

Read this support article about managing membership of a family sharing group --> Leave Family Sharing - Apple Support

You may wish to note:

Legal - Apple Media Services - Apple

D. "Family Sharing Rules: You can only belong to one (1) Family at a time, and may join any Family no more than twice per year. You can change the Apple ID you associate with a Family no more than once every ninety (90) days. All Family members must share the same Home Country."

Does the new son violate any of those rules?

Have you tried inviting them?

Set up Family Sharing - Apple Support

Invite people to join your family

If you choose to invite people later or want to add another member to your family, you can send an invitation via Messages, email, or in person.

I don't see any mention of how it builds up an initial suggestion list.

i have no idea then. I don't actually use Family Sharing myself and I don't recall ever seeing anybody else with this issue.

Refer to this page for Apple Support features ➔ Contact - Official Apple Support

See if there is a chat or phone call contact method offered lower on the page (you sometimes have to narrow down the options multiple times before this is shown). If you do not see your issue, keep experimenting with any series of selections until you reach one that offers a chat session or a telephone call and get the representative to redirect you.

This support article has various country telephone numbers for contacting Apple for support and service ➔ Contact Apple Support - Apple Support For some countries look under “Other” listing at the end of each region. Not every country has telephone support.