I have the same problem. I'm running with a 3600x and 5700XT Pulse. The problem started about a week ago and here are a couple of things that cause the "stutter" or FPS drops.
1. Playing Warzone and I can't watch YouTube on Chrome. I used to be able to have Warzone (and other games) running while playing a video on the background with no problems.
2. I can run Classic WoW (Windowed fullscreen) as soon as I turned on the PC with absolutely no problems. I'll play some R6 Siege with no problems. But if I then go back to Classic WoW, I CAN'T play in Windowed fullscreen again as frame drops to around 20-30 FPS (from 260+ average). The problem "fixes" itself when I alt-tab, open a window, or play in Windowed mode (not Windowed fullscreen). I could run Classic WoW + Warzone/Siege simultaneously without any problems whatsoever.
3. Games seem to be running a bit heavier lately, I can't really explain it. It almost feels like there's a bit more input lag even if FPS don't reflect any changes.
I'm not sure what is causing it, but I think I was already running the latest drivers before the problem started. I also don't have automatic Windows updates and I don't think I updated before this started happening.
Stutter/frame drop problem - YouTube
EDIT: ++ Possible "fix"++
A friend suggested to turn off instant replays/recordings and such because Shadowplay (he owns Nvidia) has been known to have similar problems. I turned off Instant Replays and Record to Desktop, and the frame drops were 100% gone. I then turned ON Instant Replays while leaving Record to Desktop OFF, and I still had no frame drops.