First, you are behind on Ventura updates. Make sure Ventura is fully up to date. I believe 13.4.1 is the most recent version.
Second, beginning with Ventura, you must now approve any newly connected external devices before they will become available on the USB-C ports. You can modify these settings in the Ventura System Settings under the "Security & Privacy" section. I have the option "Allow Accessories to Connect" option set to "Always when unlocked" so I am not prompted for confirmation if I am logged in at the time an external device is connected, but there are other options as well....but my setting or "Always" is good for testing devices which are not currently working to avoid an issue with being prompted while trying to figure things out.
Also, make sure to try using another USB-C cable and adapter, plus try using another USB port on the Mac. Disconnect all other external devices in case one of them is causing a problem. And connect the Ardruino directly to the computer.
I'm not sure if booting into Safe Mode will help since you need a serial driver to load, but it is worth a try.
If you have any anti-virus apps, cleaing/optimizer apps, or third party security software, then uninstall them by following the developer's instructions since these types of apps are not needed on a Mac, plus they tend to cause all sorts of problems....possibly even not being able to access the Arduino.
If none of these things help, then you will need to contact Arduino support or check with the Arduino community for any known issues involving macOS and Ventura specifically. They will most likely be the ones with the answers you seek since very few people reading these Apple forums are likely to being an Arduino (especially that specific one) whereas the Arduino community is likely using all sorts of computer and operating systems including macOS. Keep in mind, this Arduino board may actually be defective, or perhaps there is even some known issue which occurs under certain circumstances....the Arduino community will be more likely to know these things than the general Apple community.
Issues with third party apps and third party hardware are usually the domain of the third party to support you and assist you in getting the third party product to work. Apple only provides the OS and the device. If macOS is at fault, then the third party vendor is responsible for raising the issue with Apple so that between them hopefully a fix is implemented in some fashion.
Now if you are told by the Arduino community to perform a certain general action and you are not sure how to do that under macOS, then that is something the Apple community may be able to assist and interpret for you.
I can tell you that getting some third party devices to work under macOS can be tricky sometimes...even more so with all the new security settings & features macOS has implemented in recent years.
FYI, I'm not even sure what app your screenshot is even referencing with those menu options. It would help if you had mentioned this detail.
Does this Arduino require a built-in macOS serial driver, or does it require a third party driver? If a third party driver, was installation even successful? I know I've had issues installing third party drivers several years ago because Gatekeeper would not fully allow the driver even after repeated attempts.....things have only gotten more complicated since then with the new security features.
