Hi,
The HP downloads page for the HP Photosmart 2610 All-in-One Printer appears to have drivers for older systems only.
You could try resetting the printing system and re-adding the printer. Does the operating system suggest a driver to use? If so, carry out a test with that driver.
Reset the Mac printing system to solve a problem - Apple Support
Add a printer on Mac - Apple Support
If nothing else helps, you may want to check whether the (Dec 11, 2020) updated HP Printer Drivers v5.1 for macOS package download from Apple at https://support.apple.com/kb/dl1888?locale=en_US would work. Reset the printing system. Verify that your printer is recognised. Is there an appropriate driver to use (perhaps something like the HP Photosmart 2600 series 2.0.4, or another similar HP printer)? Look upon this as an experiment. It may not work. There is always a certain risk involved with an experiment. Software conflicts cannot be ruled out. Data may be lost. A hardware problem is unlikely, but it is impossible to guarantee anything. Make sure that you have multiple backup copies of important files before you start.