I checked my project and it's still working without a problem for me.
Please check if the steam overlay was injected correctly:
- Do you see the steam popup in the bottom right corner, when you start the "Hello Steamworks.Net" project?
If not then the overlay wasn't correctly injected.
Please open the task manager (while the project is still running) and look for a process called "gameoverlayui.exe". It will only appear if your steam client and the project is running and when the overlay was correctly injected.
If this process doesn't appear in your task manager, then it's necessary for you to start the project from within your steam client. This should inject the steam overlay correctly.
For that you need to add the project as a "Non-Steam-Game" to your games library and start it using the play button in steam.
Latest now it should work.
Note: I had the same problem like you in a WindowsDX project, because the overlay gets differently injected in a DirectX project. Starting the project from within my steam client resolved this issue.
Facepunch.Steamworks seems to be a good and solid implementation. It is also mentioned in the official Steamworks partner documentation (like Steamworks.Net). A big plus with this library is, that you can code in native C# without the need of calling functions from the steam api.
Unfortunately I didn't make any experiences with it so far. So I can't help you with that.
Nevertheless I hope that the advices were helpful.
PS: Please make sure to use the latest GitHub version, because at some point I switched from a WindowsDX sample to a DesktopGL sample as a result of the overlay error in a debugging session I mentioned above (overlay is working on all platforms when starting the project from within the steam client).