Keep in mind that Messages are all controlled by your iPhone. Whenever I have had issues with Messages on macOS, I have either had to reboot the iPhone, update iOS on the iPhone, or turn off Messages on the iPhone, then re-enable Messages on the iPhone. Many times it also involves rebooting my Mac with each change on the iPhone as well. Sometimes I even quit the Messages app on macOS so it would have to relaunch....sometimes prompting me to log in again, but that issue was many years ago when I was using Catalina.
FYI, I have no issues using Messages on Ventura or even Big Sur which is two versions/years older.
What exact issue are you encountering with Messages on macOS Ventura? What is the exact error message?
Your iPhone Messages configuration settings needs to be configured properly as well.
If you are using any third party anti-virus software, cleaning/optimizer apps, or third party security software, or VPNs, etc., then any one of them could be causing your problem since they all interfere with macOS at a very low level and are known to cause all sorts of system issues. If you have these types of apps installed, then uninstall them by following the developers' instructions.
It is also possible you have some sort of networking issue going on....after all the Messages app on macOS needs access to the Internet for the necessary protocols it may be using and access to your iPhone & AppleID (aka Apple's servers).