GP here. Diet and Zero sodas simply use artificial sweetners, which have come a long way over the years. You'll hear some people say nonsense like "it's just as bad/worse than regular soda!", and others that will say "it's like drinking water!". Of course, the truth is somewhere in the middle.
Popular artificial sweetners like Sucralose and Aspartame have been shown to at least correlate with metabolic syndrome/obesity/insulin resistance (and thus eventually diabetes). This is pretty much undeniable. However, they are still much, much better for your metabolism than regular sugar, and they indeed are not metabolized as carbohydrates and don't contain any calories.
There's also the "cancer" argument, which did apply to older sweetners in outrageous quantities (some of which were unrealistic/literally impossible to consume). As of right now, there's no evidence that shows artificial sweetners currently in use, consumed in moderation, cause or correlate with cancer. This may change in the future as more studies become available. Also a lot of the evidence against sugar replacement was funded by, you guessed it, sugar lobby.
In short: They're still bad for you. They're much better than sugar for you. They mostly don't have any calories and are not digestible carbohydrates. They probably don't cause cancer if used in moderation.
Fun fact: I've sustained high ketone levels while consuming coke zero freely.
^ That. I read so many government published studies on nih.gov and all studies show both ends of the spectrum, with some saying it's linked to health issues, and others saying it's linked to health issues because the type of people that drown in diet drinks are the ones who continue to make poor choices anyway... Truth is definitely in the middle for sure- in moderation, along with eating healthily, it's fine.