Hi Denis,
There are a few things that come to mind, but let’s start by double checking your workflow…
Before we jump into that, note that the Registry hacks you posted are all R20.1 which is related to AutoCAD 2016. AutoCAD 2022 would use R24.1
Workflow Sanity Check:
Straight out of the box, ProjectWise-Integrated Civil 3D will look like this when you try to create a New Data Shortcut Project Folder

So the first thing you need to do is Set Working Folder

This should result in a prompt for ProjectWise Datasource Log In

Once you have logged into your ProjectWise datasource, you will be asked to choose a folder which will become your Civil 3D Working Folder. This is where the New Data Shortcut Project Folder will be created. Note that once it is created, the name that you give it will become the name of a file with a .CivilDSProj file extension.
For this example, I’ve chosen _L00_CivilDSProj as my Working Folder

Now that the Civil 3D Working Folder has been selected from a location in ProjectWise, you should be able to create the New Data Shortcut Project in that location.
Right-click again on the Data Shortcuts node from the Prospector and this time when the New Data Shortcut Folder dialog box pops up, the Working Folder should be pointing at the location that you selected in the previous step.
It should be apparent that it is integrated with ProjectWise because the directory path will begin with pw:\\

Be sure that you are not using special characters in your naming convention, and keep the name short.
Civil 3D doesn't like long directory paths so the shorter you keep your Data Shortcut and Data Shortcut Project names, the better.
If you are following this same workflow and it does not yield the same result, let me know.