Heureka!
I made a progress (successfully installed the correct drivers - bumblebee version - they now even show properly as installed in the System -> Manjaro Settings Manager -> Hardware Configuration), but that returned me full circle to my very first post:
When I try to open the GreenWithEnvy, it still says:
NV-CONTROL X extension not found
It was not possible to find the NVIDIA NV-CONTROL X extension on the current Display device.
Please make sure that the NVIDIA proprietary display drivers are installed and they support your current GPU
Reason Why I installed Optimus is because I found that as a solution to this problem somewhere on a forums here. So how can I properly install the NV-CONTROL X extension?
I will post how I installed the proper drivers - it might get useful to someone down the line, I had to put it together from various posts:
How to uninstall Nvidia drivers when you have a black screen after OS has been loaded:
1.) You need to TTY2 into the system while booting OS (just when the Manjaro logo will pop-up):
Ctrl+Alt+F2, - use the same command again if you end up on a black screen and nothing is happening
2.) use your credentials and log in
3.) once inside, see what you have installed:
sudo mhwd -li
4.) If you will try to uninstall it now, you will get error:
Error: config 'video-nvidia' is not installed!
To avoid that, try adding the ibt parameter:
sudo nano /etc/default/grub
and in this line: GRUB_CMDLINE_LINUX_DEFAULT inside the quotes, after a space, add this parameter:
ibt=off -Dont remove anything from there!, just add it to existing parameters, save the file (Ctrl+O, then Ctrl+X to exit nano), update grub:
sudo update-grub
reboot
5.) Now you should be able to uninstall the driver:
sudo mhwd --remove pci [video driver name]
6.) install the proper nvidia drivers, then reboot:
sudo mhwd -i pci [video driver name]
in my case:
sudo mhwd -i pci video-hybrid-intel-nvidia-390xx-bumblebee
7.) Reverse changes from step 4