HP Support – Welcome to the product support page! Samsung CLP-320 Color Laser Printer series
"HP Print and Scan Doctor is no longer maintained and should be removed due to potential security risks."
Under Software and Drivers, there are no selections for macOS – only for Windows and Linux. ("If your operating system is not listed then HP may not provide driver support for your product with that operating system.")
The User Manual does mention the Macintosh. It lists the system requirements as
- Mac OS X 10.3 – 10.5, on PowerPC-based and Intel-based Macs.
- Mac OS X 10.6, on Intel-based Macs
I can pretty much guarantee that any driver written for those machines and those versions of macOS will not be compatible with Apple Silicon Macs. (Rosetta 2 can't translate PowerPC and Intel kernel extensions.)
Your Mac is Intel-based but Tahoe is FIFTEEN major versions ahead of Snow Leopard. I think it's very likely that there have been changes that would keep a printer driver designed for Snow Leopard from working under Tahoe.