sj60,
Sorry to read about your troubles.
The packages on Synaptic are not printers - they are drivers and supporting files. If you remove one (or more) driver for a printer it simply means that the printer may still be recognized by Zorin but would use whatever remaining drivers it finds available.
In contrast, the system recognizes printers and displays/manages them using lpadmin and lpstat.
My intent was to remove any conflicting drivers because that seems to be what is interfering. Hence, removal of whatever you had installed before. When I read that you had problems installing Synaptic, I realized your updates weren’t being pulled from the correct repositories, hence my subsequent post on the Updater. That would also imply that Zorin’s driver may have been able to help you print properly without the need for the external HP driver but the Zorin driver was not given a chance since your Software Updater wasn’t updating properly. Since you had already installed the HP driver, I naturally suspected that was causing interference between printing and scanning. Note that once we corrected the Software Updater, the Zorin driver may have also loaded while the HP driver was also already loaded (partially or otherwise) on the system.
Given all that you have been through, I completely understand if you decide to troubleshoot yourself. I can only suggest that to start from a baseline, I recommend removing all Samsung drivers listed on Synaptic and removing all printers using lpadmin. Also make sure no printers are showing under Zorin menu -> Settings. I only suggested lpadmin because you stated that you are unable to permanently remove the duplicate installed printers using Settings. With this clean slate, and all updates installed from Software Updater, then plug your printer back in to the computer and see what happens. That is the only way I can think of to conclusively eliminate any interference from multiple installed drivers. However, it is just a suggestion.