Hello,
This is a known issue, documented in the Xcode 16 beta 3 Release Notes.
Xcode will fail to launch for some users. Users who have not installed Xcode 16 beta or Xcode 16 beta 2 will see a “Loading a plug-in failed” alert. (131066390)
You can either install Xcode 16 beta 2 prior to installing the beta 3, or you can open the terminal and select Xcode 16 beta 3 with
xcode-select -s $PATH
Then run
xcodebuild -runFirstLaunch
and Xcode should be able to launch.
Let us know if that doesn't resolve the issue for you!