hplip requires pyqt4
Solution 1:
You're probably going to have to completely reinstall HP printer support because you removed everything involving HPLIP. You probably will need to go to the HPLIP page and download, and install, the latest HPLIP. If you're able to do this, it will set up your printer and then give you the opportunity to install the correct plugin that will enable all of your printer's capabilities.
You might have avoided so much trouble if you had started by running the command N0rbert gave you, before you did anything else:
sudo apt install hplip-gui
(I know, you didn't know that then; I learned it the hard way, too. This works because HPLIP is already installed on Ubuntu, but not the GUI, which you need in order to get the plugin.)
Then run "HPLIP Toolbox" (I run it from the Dash, but you can run it from the command line, too). This will open a GUI which will give you the opportunity to install a required plugin. Many HP printers require this plugin to be installed in order to perform certain functions (such as scanning and faxing).
I have to do this every time I install a new version of Ubuntu (or reinstall) because my HP printer is one of those that requires a plugin, and it appears yours does, too. Plugins are not loaded by default, and unfortunately little information is provided anywhere about how to solve the problem.
Solution 2:
HPLIP supports Qt5 from 3.16.5 and above
To enable qt5 support
You need to install the following dependencies
PyQt5
python-qt5-dbus
Go to source of hplip. By default its in ~/Downloads.
Run the following commands
./configure --prefix=/usr --enable-qt5 --disable-qt4
make
"make install" as root user