Not sure if this will help your specific situation with Steam, but I had this issue on PC through EA app. It was a factor because we had to have the EA app overlay disabled due to the interactions with the game it had on a multiple monitor setup, making the game unplayable. Side effect was that the friend request notifications wouldn't show in-game. What we had to end up doing (that I read in another forum somewhere) was that one player went in-game, and invited all the others to the party out of game, but signed into the EA app. A notification would appear for them and give them a few seconds to accept and launch or ignore. This is the only way we've found to be able to do this. Hopefully it helps others to see this!
