When I tried to launch Unreal Engine, the following error suddenly appeared and Unreal Engine would no longer start.

The solution was exactly as written in the error message, but I could not find much information when searching for it, so I am leaving this note for my future reference.
In my environment, the issue was resolved by running the following command, as indicated in the error message:
$ xcodebuild -downloadComponent MetalToolchain
Beginning asset download...
Downloaded asset to: /System/Library/AssetsV2/com_apple_MobileAsset_MetalToolchain/058e1b31129b642e40598a87b55aa54b2a29e538.asset/AssetData/Restore/022-21521-014.dmg
Done downloading: Metal Toolchain 17C7003j.