Hp offficejet j4580 failing to install with HPDM

asi said in the title, I have a HP Officejet J4580 (which supposed to work with hplip, according to here: hp's Developer Portal | All Supported Printer Models)

and hp-setup also does find the printer (USB connected) but does not install it properly.
This means, the GUI shows the right printer, and I can select it, but when I proceed to next setup step, HPDM just doesn’t do anything and leaves empty.

In addition running CUPS web interface at localhost won’t let me in - it just keeps showing me the login window after entering my credentials - no clue what’s going on there)

here is the output of hp-setup, if that is helping:
>> hp-setup

> HP Linux Imaging and Printing System (ver. 3.20.11)
> Printer/Fax Setup Utility ver. 9.0
> Copyright (c) 2001-18 HP Development Company, LP
> This software comes with ABSOLUTELY NO WARRANTY.
> This is free software, and you are welcome to distribute it
> under certain conditions. See COPYING file for more details.
> Warning: Ignoring XDG_SESSION_TYPE=wayland on Gnome. Use QT_QPA_PLATFORM=wayland to run on Wayland anyway.
> "/proc/18892/root"
> Searching... (bus=usb, search=(None), desc=0)
> Traceback (most recent call last):
>   File "/usr/share/hplip/ui5/setupdialog.py", line 1329, in NextButton_clicked
>     self.showAddPrinterPage()
>   File "/usr/share/hplip/ui5/setupdialog.py", line 729, in showAddPrinterPage
>     self.readwriteFaxInformation()
>   File "/usr/share/hplip/ui5/setupdialog.py", line 1152, in readwriteFaxInformation
>     self.fax_number = to_unicode(d.getPhoneNum())
>   File "/usr/share/hplip/fax/pmlfax.py", line 146, in getPhoneNum
>     data = utils.printable(self.getPML(pml.OID_FAX_LOCAL_PHONE_NUM)[1])
>   File "/usr/share/hplip/base/utils.py", line 958, in printable
>     return s.translate(identity, unprintable)
> TypeError: str.translate() takes exactly one argument (2 given)
> zsh: abort (core dumped)  hp-setup

I recently discovered that my CUPS service was disabled. You can try with:

sudo systemctl enable --now cups

maybe I was not precise enough, I can reach CUPS web portal, but cannot login somehow, see picture below.
When I click “Add printer”, I am prompted for login, I enter my credentials (the correct ones, of course) and all it does is prompt me again.

I think hplip is not installed correctly .
Try to uninstall and reinstall it.
I use octopi or terminal

sorry for the delay, removing and installing HPDM was not the solution.

What bothers me the most is, that with previous Ubuntu-based ZorinOS installation, this printer worked plug&play, so to say.

is there a way to “compare” these distros in terms of packages or drivers they use?