It looks like the Visual Studio Code PowerShell extension is only able to debug scripts running on PowerShell Core.
Is it possible to debug PowerShell scripts when running PowerShell 5.1? I need to debug scripts accessing Active Directory.
On Windows, yes.
https://code.visualstudio.com/docs/languages/powershell#_multiversion-support
TL;DR: Just click the version number in the lower-right corner.