What exactly do you mean by:
debug the CLR stored procedure without deploying it on SQL server
? The code only runs in SQL Server. It needs to exist within SQL Server in order to be callable as the environment that calls it is SQL Server. Visual Studio comes with SQL Server Express LocalDB so that you can easily test stuff like this on your local dev box without having to deploy it anywhere outside of your personal dev environment. When you create a database project, the debug connection string (i.e. where it deploys to when publishing to test, whether you start debugging or not) should be preconfigured for your local instance of LocalDB.
Please try the steps I outlined in my answer to "How to debug a CLR Stored procedure in VS 2013". That was tested on VS 2015, and I expect the behavior to be the same in VS 2019. Either way, that answer contains some required steps that are missing from the MS documentation.