In that case these are the following options that should be available on both console.DF made a case for MS to keep the display settings as is. DMC5 on the PS5 offers no way to cap the frame rate. Technically the same is true of the Series X but because you can change the settings on the console you can limit the game to 60hz instead of it trying to run at 120hz all the time.
EDIT maybe a auto mode for refresh rate would be prudent.
-Option to cap frame rate at 60 and 120hz at a system level.
-Option for games to override system settings so that I don't have to change system level settings when switching between games.