At step 4, instead of opening the website in Test Server IIS, use the Visual Studio "File -> Open -> Open Website..." option and navigate to the folder on the remote (APP) server that has the website you want. You will probably want to map a drive on Test that points to that location on APP to make this part easier.
Once the website files from the APP server's folder are loaded into Visual Studio on TEST, right click the project name there, and on its property page in the Start Options, under "Server" click "Choose custom server" and put in the URL of the website that is running on the APP server.
Open the website link in browser. Then in Visual Studio carry on with your step 5 and attach to the w3wp.exe process. If you don't see it still, select show for all users.
Figured this out based on
Remote debugging - Visual Studio | Microsoft Docs[
^] and the last post at the bottom of
debugging - How do you debug classic ASP? - Stack Overflow[
^]