asp.net websites did not use project files. dll's were manually added to the bin or more common the gac. (nuget did not exist at the time). websites used the aspnet compiler. and the code behind files are compiled at site load. all runtime binding information (say a gac reference) is in web.config
you can google for old articles on converting a website to web application (project file).
note: to run an old websites on a new machine, you may need to install some assemblies in the GAC (say ado.net). look in web.config for references. you will then need to find the old installers.
https://learn.microsoft.com/en-us/dotnet/framework/app-domains/working-with-assemblies-and-the-gac