For upgrading PostgreSQL from 15 to 16 manual user action is always required as this is AFAICT not done automatically. And when not doing these steps the user is left behind with unsupported and unmaintained PostgreSQL server packages which has even security implications.
See the following posts below for a few additional notes. I had suggested to ask the Kali team (or even Debian as Kali is AFAICT also only taking the PostgreSQL packages from Debian) for better documentation around this topic as users seems to struggle quite often with this (Greenbone software unrelated) administrative tasks.