project explorer shows the loaded project. to load a project pick file->open -> open solution/project, and pick a project file or solution file.
to create a core webapi project, you can do it from the command line, in the folder you want to create the project (the project will be named the same as the folder).
dotnet new webapi
or in vs to create a new project, in the project template in the search enter webapi. pick the c# or f# core template