Adding to the drop down menu I screenshotted below, it would be really helpful to specifically see games that belong to a group.
This would be very practical for war clans and group communities in general to be able to quickly find other groups to engage with, or find places that specifically involve themselves in a structured community.
A simple “Add to profile” button and “Remove from profile” button which can only be used by group members who have a high enough permission level to edit the game. This would work well imo. If you get demoted in the group/leave, it is automatically removed from your profile.
Say 3 people equally worked on a game, they could all 3 showcase it on their profile. In fact, this used to exist because I had all my group games on my profile in the past.