A friend on Discord gave me the solution to this problem.
Before you package a program in UE 5.1.1, you must 1) delete all unnecessary folders prior to packaging in the editor. But keep the Config and Content folders, along with Plugins and Source if you have those. Delete these folders before you open the project file.
Also, for those who don’t know and are migrating from 4.27 to 5.1.1, you will have to manually configure the Packaging Settings or some files might be missing. You want to make sure needed files and content are included before you begin packaging. And update the SDK if necessary, too.