This HP support page:
https://support.hp.com/us-en/drivers/selfservice/hp-photosmart-c4500-all-in-one-printer-series/3575173/model/3575174
suggests that printer does not support higher than macOS 10.11"El Capitan," which was replaced five years ago. The last updates HP pushed out for that model were in January 2014, so the "obsolete" issue is likely at play. I think you need to either chat with HP or shop for a new printer.
However, often old unsupported multi-function device software will print, but not do any of the other functions like scan or FAX when the macOS outgrows the old printer software. This article in the one Claire linked is a good test of whether only the scanner function is unhappy with the new OS:
Scan images in Image Capture on Mac - Apple Support
If it scans with Image Capture, which is pre-installed in macOS, you can keep using the C4580. I've not used a printer's scanning software package in years. With either our old HP 6280 (R.I.P.) or our current Epson XP-830, Image Capture does such a good job, I've not needed the printer compnaies' software to scan well.