It is not always a given that the GCam port (from the Pixel camera app) is actually always better than the stock S23 Ultra app, for example, some say the 10x optical zoom, and the low light photos, are better with the stock app. But in other cases the blue sky colours can be better with the GCam ports, and also the GCam ports don’t overprocess as much as the stock camera app does (resulting in softer, finer detailed photos).
The other complicating factor is there is no one GCam port to just install and use. There are a number of them with some slightly different features, and also some may not even work on your device. So, unfortunately each person would have to do some research, and even test possibly more than one port.
GCam ports have been renown for their excellent HDR+ feature since the early days, and they would likely improve photography on most phones that they can install on (not just the Samsung Galaxy phones). The other plus is, you do not have to root the phone, and the stock app is still there to use.
There are actually quite a few videos comparing the stock vs a specific GCam port.
See https://cyanogenmods.org/samsung-galaxy-s23-ultra-gcam-port/