is InstallAssistant.pkg a legitimate mac installer?

Yes, it’s available on Apple’s developer site.

Is there a specific reason for using " InstallAssistant.pkg " for Ventura ?

Perhaps if you elaborate further we may be able to offer alternative methods

If you get the package directly from Apple, then yes it is a legitimate way to install macOS.

The .pkg will unpack into Applications -> Install macOS Ventura, and from there you can complete the install. While "Install macOS Ventura" will delete itself when it finishes, you have to manually delete the .pkg file if you want the 12+GB of storage back.

As mentioned by both previous Contributors - if it were Directly from the Apple Developers site - proceed with the instructions from @Bob Harris