I'm also having frustrations with Ventura and Lighroom printing. Yesterday I updated LR and MacOS hoping the problem would be gone, but it remains (now at Ventura 13.3.1, LR Classic 12.3). Printing with Epson P800, driver 12.62.
My main problem is that print settings don't stick. After selecting printer settings: media and page setup in LR, after closing dialog box, when I open it again, often different media is selected, or page setup goes from "borderless" to "roll paper."
I've tried deleting presets, not using presets, restarting Mac, and other troubleshooting steps, but issue remains.
If anyone has any suggested fixes, please let us know.