Hey Jay, I'm wondering if it's because the initiative you're looking for is not in the content library (first image). All initiatives have a content library (a default ArcGIS Online group called initiative-name content group) to which the initiative site is shared. So if you're looking for an initiative site in another initiative's content library and that initiative wasn't shared with the content library yet, it won't appear.
Doesn't seem like it. I shared this Initiative to the InitiativeName Content group and it still doesn't show up in Hub, Initiatives (second image). I don't see anything different about how this is configured that would explain the difference between it and other Hub Initiatives that DO show up. Doesn't seem to be negatively affecting the site, so I guess I won't worry about it too much.