Thanks for the helpful suggestions. When I try to enable Web Services from the printer itself, it says "Web Services (ePrint and Apps) could not be enabled." I don't know why -- as far as I know, the printer is connected to the internet via Ethernet.
On my Mac, when I try to use (what I take to be) the Embedded Web Server to enable Web Services, it goes through the steps and then says "Web Services is not enabled." Maybe something is off about the way the printer is connected to the internet. Or maybe I have to do something with Proxy settings, but I don't know what that is.
I also found a utility called "HP Firmware Updater" on my computer, but when I try to use it, it says that "firmware updates are not yet available for your device." But maybe that's because Web Services aren't activated.
So I may indeed have to contact the HP Support team, but am not sure what they would do for an out-of-warranty printer or how much it would cost.
Thanks again.