While backward compatibility on Xbox Series X/S has allowed users to have a seamless experience, things are getting a little better on PS5.
Activision recently released a new patch for battle royale, adding support for 120 FPS performance on PS5. Players can now enable this setting. But to enable this setting, you will need an HDMI 2.1 screen.
Call of Duty: Warzone is available on PS4, Xbox One and PC. It can also be played on PS5 and Xbox Series X/S with backward compatibility.