In the Nvidia panel under Manage 3D Settings, go to Program Settings, Halo: The Master Chief Collection and search for the option Low Latency Mode and set it to Ultra. Im sure AMD users have something equivalent. It fixed the horrendous input lag for me.

What FPS does Halo MCC run at?

120 FPS According to Microsoft, the Master Chief Collection has been fully optimized for the Xbox Series consoles, which translates to 120 FPS gaming in campaign and multiplayer modes.