First step is to go to
http://www.openprinting.org/
There you scroll down and find a link to the "Driverless Printers" list.
Click "Browse". You get onto
https://openprinting.github.io/printers/
into the search field enter "Envy 553". The last digit does not matter.
Different last digits usually only mean different power plugs for the
different destination countries.
So your printer supports AirPrint, one of the driverless IPP standards.
Your printer's Wi-Fi is flaky, so use IPP-over-USB. Keep the printer
connected to USB and install the "ipp-usb" package. Having done this
your printer should appear already in the print dialogs of many
applications.
If not, create a driverless print queue:
First, run
driverless
You will get an URI for your printer, most probably
ipp://localhost:6/ipp/print
Create a driverless queue with this URI:
lpadmin -p envy -E -v ipp://localhost:6/ipp/print -m everywhere
Now all your apps should show your printer with queue name "envy". Can
you print on this queue?
Till
P. S.: Avoid HPLIP if you do not REALLY need it.