You could play Ghost Recon: Wildlands or try some of the older Ghost Recon or Delta force games. Some of the weapons on offer are older in it.

There’s a tag on Steam named coop campaign that might help find a few for you. I saw a real time tactics game called War Mongrels that might be of interest though it’s obviously not a shooter.

Also, obviously there’s “hell let loose” but it’s not a campaign experience