On the News webpart of my hub site (using Hub News layout and showing posts from all sites in the hub), any post that I order manually under Organize does not follow my audience targeting rules. Any non-organized posts do correctly follow my audience targeting rules. I followed the instructions shared in https://techcommunity.microsoft.com/t5/sharepoint/audience-targeting-for-news-not-working-at-hub-sit... - I turned on Audience Targeting for the News webpart, Site Pages library of the specific site in the hub, and the Site Pages library of the hub site itself. Thank you for your assistance!
I was under the impression that this was the expected behavior. If you specifically tell your news webpart to show a specific story in a specific position, I thought it was supposed to ignore your audienceing and show that story in that position.