Haven't even heard of Faugus until this post, so I won't be able to sell you on it.
I used Lutris for quite a while but had to drop it because there's some really bad network coding in there that causes it to essentially DDoS my DNS server if it can't give what it expects. For example, when I had installed Dead Space Remake, it was looking for OG assets, which has been moved to a new location, and Remake took that original location. It was sending well over 1000 DNS requests a second for several seconds before my DNS server would 10 min blacklist my PC. If took me 2 weeks to figure out exactly what was happening because I wasn't noticing it was Lutris specifically and was thinking my NIC drivers were killing my connection.
I moved to Heroic and tbh, I don't see anything in Faugus that Heroic isn't already doing. I have GOG, Epic, and Amazon games in there, cloud saves with GOG, achievements with GOG (but no pop-ups), and they've been using umu for a long time. Also automatically adds my games to Steam with assets. They also have a Wine manager and will actively check for game updates.
Does anyone know what Faugus does better? I'm interested, but like OP, I'd have to be sold on it too.