Incredibly, it seems that using an O365 Group to share an app is not yet a thing.... I cannot think of any reason why it shouldn't be given that almost every new Office 365 service provisions an O365 group...the mind boggles.
I had been stuck trying to share with a security group and it not displaying. For me, the trouble was that we were using on-prem security groups. They are supposed to sync, but for some reason it wasn't working. My global admin went and created Azure security groups for me at portal.azure.com and within minutes I was able to share to these security groups. If you are having issues, try creating an Azure Security Group.