Figured out my problem. For anyone who is using manual signing, when you create your Provisioning Profile you need to select "Mac Catalyst" for the Profile Type instead of "Mac". I guess that's pretty obvious but be aware that when you view the profile in the portal, the App Groups capability still won't show up on the Enabled Capabilities section.

I'm having the same issue but because of CarPlay support, I had to turn off "automatically manage signing" in Xcode. When I go to the developer portal, look at my identifier, and click on the information button for App Groups it says the Platform Support is "tvOS, iOS, watchOS". I'm using the same identifier for macOS and iOS. Anyone know how to manually add the App Group capability to the macOS provisioning profile?