Unless that HP Smart application leaves you with Jan 2022 drivers for Monterey, HP has not explicitly supported this device on Ventura yet. I only see an HP OfficeJet Pro 8610 supported in Apple's built-in AirPrint (which might work with your networked device), but you may also be in that void between HP and Apple support for this device.
If Apple's provided Image Capture also does not resolve your scanning issue, then I suggest that you trial the paid VueScan Professional to see if it resolves your scanning issues on Ventura. It supports the HP OfficeJet Pro 8600 without any additional Apple or HP software.
As a note, I purchased VueScan Professional in 2010 for what was then an abandoned Canon scanner, and that device still works on Ventura with the current VueScan Professional version. In those 12 years, I have never paid for an upgrade to newer versions of VueScan, and I receive nothing from the vendor for mentioning their product here.