Note: I am using a MacBook Pro on macOS Big Sur and it has both the Intel internal GPU and a Radeon discrete GPU.
If you force the application to use the discrete GPU it works for me. I went in to the settings for the battery, clicked the Power Adapter settings on the left, UNCHECKED the automatic graphics switching option, then launched the launcher with:
open /Applications/Epic\ Games\ Launcher.app --args
and it opened and worked. While the launcher was running, I re-enabled the automatic switching setting so I wouldn’t forget. I image I may have to disable it again to launch the Unreal Editor, but I am not sure.