I do not play Overwatch but i have bothered to read most of the background stories of the characters.
As far as i get the picture there can be made many things. Like when Overwatch disbanded their facilities got raided and many weapons stolen - so one part of the "missions" can be You and your friends raid terrorist/XXX organization warehouse and get some nasty weapon back for safeguard. Or some of the heroes are involved with some shady organizations so You and your friends can be attacking branches of those organization and try to bust them etc (idk). Those Omnic dudes can get a faction going rogue and threatening to attack the world again and You and your friends go to destroy their factories for weapons etc. You can also hunt criminals.
There are many things that can be done in "PvE" mode with this world.. cool stuff... why are people so against it? :")