And YES I play multiple games at once, so Steam will tell you what I'm doing every time I click another game window! Cool huh?
Or not...
Sometimes, people tell me: "Omigosh Metal, can you stop giving me notifs PLEASE its so turrdyy..."
Well, I'm not the one giving you those notifications bro! That's Steam!
But I WILL be the one explaining you how to get rid of those <annoying> notifications, okay?
First, you go to Settings in your Steam client.

Click Friends!
Then, uncheck notifs that you dont like. Or if you really don't want any notifs at all, your window should look a bit like mine

Of course, this is just for the friends part. If you're getting all sick and tired of all the group notifications, there's not much I can do for you.
Therefore, the only option is to go to In-Game, and UNCHECK "Enable the Steam Overlay while in-game".

This will suppress ALL notifications you would normally get.
Ahhhh Finally... Some peace and quiet.
So... Alone.
Yup, you're all alone now. Enjoy it.