Overwatch has been updated by Activision Blizzard to add support for 120 FPS on Xbox Series X and S. This is not available for the PS5.
Overwatch is one of the games that is benefiting from the better backward compatibility support that is available for the Xbox Series consoles. This has resulted in games like Rocket League and Call of Duty: Warzone offering 120 FPS on the Xbox Series X while the PS5 version is left untouched. Basically, Microsoft has added enhanced backward compatibility support for their new generation consoles which allows developers to utilize additional power without releasing a full overhaul patch for their games.
Due to the limitations of the PS5 backward compatibility, there is no 120 FPS patch for several games with Overwatch making the jump the list with the most recent update that was released on March 9th.
According to the patch notes for this update, the game has been updated to add support for three different modes on the Xbox Series consoles.
So if you have Overwatch on the Xbox Series consoles, you can either play it at 4K at 60 FPS or 1440p at 120 FPS. The middle option which is balanced will retain the image-quality while rendering at 1440p at 60 FPS.