Hey there!
Printers can be tough when they don’t want to work, but there’s usually a reason and fix.
So your new printer does show up in System Preferences? And does show as available to print? (Green Light)?
Can you say all the steps you’ve tried already?
Is this both a usb and wireless printer? If it plugs in, I’m sure there’s a driver available, if not default on the OS, then from HP:
https://support.hp.com/us-en/drivers/selfservice/hp-deskjet-d2300-printer-series/1841737/model/1827322
However, likewise, from HP, at least here, it doesn’t show an available driver for Big Sur, unless I missed it.
Can you say exactly what happened with the HP Smart utility?
Sometimes old drivers get in the way also and need to be removed, but first, did you happen to reset the printing system, then re-adding the printer?:
Reset the printing system:
https://support.apple.com/guide/mac-help/reset-mac-printing-system-solve-a-problem-mh14001/mac
Likewise, if you haven’t already, I’d go through this article first:
Solve printing problems on Mac:
https://support.apple.com/guide/mac-help/solve-printing-problems-on-mac-mh14002/mac
Likewise, if a usb type issue, can try different chords/ports, etc.
And if it only doesn’t work wirelessly, (If that’s the case), I usually try to make sure they’re both connected to the same network bandwidth, (Either 2.4 ghz or 5.0 ghz), etc.
Let me know how it goes, or if there’s more information that can help!