Hello ehong,
I have checked the compatibility document, and it does say the 6510 is compatible with Ventura. There is an important update for the firmware for that device that you should consider updating.
I recently purchased a new Macbook M2 which comes with Mac OS Ventura 13.2 and had my Xerox Phaser 6510 automatically installed through Apple's "transfer old macbook" feature. I'm looking at the latest Xerox Drivers and Firmware for my 6510 and noticed they are outdated, however, I am concerned about updating because Xerox's website says "compatible with Mac OS 10.15 Catalina" which is many OS's behind mine. Is it okay to update to the latest driver and firmware even though Xerox says it's only compatible with a much older OS?