Cannot connect HP Photosmart to 2021 MacBookPro running Monterey

I am sorry you are having printer problems. If you will bear with me, I will offer some things to consider. Whenever we install an operating system upgrade or some OS updates, printers and scanners will often stop working. Then a new OS compliant printer software must be installed. Experience has shown that many printer manufacturers are very slow to provide updated drivers. Drivers for some older printers are never provided. What we can do is to thoroughly check the printer web site for an updated driver that works. If one is not available, then we should ask when one will be released. If that doesn't work, if the Printer has the Air Print feature, that can be used and no driver will be needed. If not, then you can check the respected web site below where volunteers write free drivers for older printers which are no longer supported, but which work with newer operating systems. It is worth checking out. Good luck.

Gutenprint Supported Printers

Yo are most welcome. Air Print is a nice advancement. It does not require any print drivers.