the default install of VS 2022 does not include the old framework, but you can install support. Unlike .net core, the old framework was very loose on version support. you can override in the web.config the version used. It will build, it just crashes if there is an incompatiability. VS 2022 will work as well as an earlier version. Some of the older designers if used may need to be installed.
you indeed may be using a nuget package that is no longer published. You just need a copy of the binary dll. Your app may also be using components only installed in GAC (especially before framework 4.5). Of course on a new machine, they may not be installed. You will need to track these down so they can be installed on the server separately. your package may also have been from codeplex which was used before nuget became popular. Unfortunately MS shut it down. there is a an attempt at an archive: https://codeplexarchive.org
once you get it to build and run, I'd update all the projects to 4.8. This also involves updating the nuget packages. This is less than trivial if some of the projects are pre 4.6. You should start with the master web project first. Updating the project file, config and nuget from 4.5.1 is rough. It's probably easier to create a new 4.8 web project and add the source code and nuget packages.
once the web project is 4.8 you can start updating the library projects. again you probably want the new project format, so create a new library and add files.
if you are using membership, be sure to read release notes. the encryption defaults changed, so you need to force the old behavior.