Wikipedia says that Overwatch and Apex Legends are each part of the “Hero Shooter” genre (boy does that sound like an uninteresting genre). I’m guessing there are greater subdivisions of play structure that matches what you’re describing, but it all sounds like an uninteresting blend of character based FPS, like multiplayer Borderlands. I guess that’s where modern gaming is, though, since these really took off after 2016, which is solidly after my “hardcore gaming” days were mostly over.