in the new project style, which supports building multiple framework versions, the build is always under the framework folder name. nuget package references are in the project rather than a separate file (packages.config)
there is no downgrade tool. the easiest is to create a new class lib with the version you want. add in the nuget packages, and the source code.
note: the extended support of vs2013 ends 4/9/24. net 4.* < 4.8 support has already ended. for security reasons you should upgrade to 4.8