Dell Color Laser 1320c with Mac OS 10.15 Catalina and Network printing
Unfortunately, you're out of luck.

The problem with these low cost, entry level printers is that they use the host (the computer driving the printer) to supply the engine for it.  

According to the specs (available as a PDF), the Printer Language is "host based."  So, it's significantly more than a driver or a CUPS PPD file - it's actual software driving it.  Because this software is (most likely) 32bit, there's no chance it's going to run on Catalina.

So, your options are limited:


Set up a small, cheap computer (like a PC running Windows 7 or 10) or even a Mac mini running Mojave or earlier and share the printer over the network - basically make a home grown print server.
Downgrade to Mojave
Buy a new printer (if you go this route, don't get another host based (usually consumer grade) model.  Get one that a corporation would buy.  Yes they cost more, but you won't run into these issues (I've got a Lexmark that 15 years old still running with zero issues).