Controlling settings, permissions, and membership within Teams and channels
Dear Grady T,
Greetings!
Thanks for posting to this community.
Based on your description, I understand your query about "Teams Private Channel in which only owners can post".
Yes, you are right! According to Overview of teams and channels in Microsoft Teams - Microsoft Teams | Microsoft Learn, this setting is under Moderation which is available in Standard channel but not in Private and Shared Channel.
Appreciate your patience and understanding and thank you for your time and cooperation. I wish you all the best!