I have the same problem with my HP Officejet 5605z. This model is not featured by the above mentioned Hannah software. In another forum I read, that a user was able to solve the problem by uninstalling and reinstalling hplip. I did so. This did not initially solve my problem. However, in the installation log in the terminal it also says:
hplip-doc hplip-gui python3-notify2
(German for recommended packages). I installed these, in particular to try the gui.
Subsequently in the Elementary OS Apps searchbox it shows "HPLIP Toolbox". This I opened.
Here there is a guide showing on how to setup new devices, which I did. I was able to add my printer (was automatically recommended) and print a test page.
Now I tried to go to my desired documents and print one of them. In the print wizzard there are now two additional entries, the middle one successfully prints my documents now.