"Correlation does not equal causation" is the commonly-used phrase, and this is a questionable-cause fallacy.
That said, if you're being really pedantic, we don't have the ability to truly know that anything causes anything else. If I let go of a ball and it falls to the ground, I can't be entirely sure that I caused it to fall (and/or it fell due to gravity). Even if I repeat that a billion times, I'll still just have correlation, not causation. But yet, we still accept causation happened here, because that's the simplest explanation for the evidence.
The problem comes in when you conclude causation, but you haven't put much work into trying to identify and account for, or remove, other possible causes, or considering reverse causation (having an injury leads to you having a cast, not the other way around). Having lots of data also helps to avoid coincidental correlations, and may identify some (but not all) other possible causes.
As the YouTuber correctly alludes to, correlational studies can have problems accounting for other possible causes or identifying reverse causation. In some cases, this might be the best we can do (e.g. it would be unethical to intentionally cause people harm, so you wouldn't be able to do a controlled study that requires this). It also presumably generally requires much less time and effort to do a correlational study, because you just have to gather the data that's already there, rather than setting up a trial or experiment to generate data. If we have a controlled study, this still can technically only give correlation, but it's much stronger correlation. Through appropriate application of the scientific method, we would hopefully get enough data to say that causation is the best explanation for the correlation (or that if we control for other variables, we conclude that there is no longer a correlation).
Side note: your link seems very biased. The actual findings on artificial sweeteners are a lot more mixed than what's presented there. They may not cause weight gain, but they are linked to increased sugar cravings, diabetes, metabolic syndrome, glucose intolerance and a disruption in gut bacteria. Although further research is needed there. (He mentions some of that, but only in the context of weight gain, whereas these things are all bad in and of themselves.) Healthline has a more neutral summary, that also links to 29 studies to back it up.
You should always be skeptical of people who say "that's what the studies say", but fail to provide any actual references to such studies (which I don't always do either, but I don't make YouTube videos authoritatively stating things, and you should certainly be skeptical of what I say, because I'm just some random person on the internet).
Also, considering that he introduces himself as "doctor Mike" at the start of the video, I feel it's noteworthy to point out that he has a PhD in Sport Physiology, for however much that is worth (beyond "to maximise gains", perhaps, I prefer to get my food-related medical advice from MDs or experts in dietary science, but your mileage may vary - that PhD is at least not that far removed from the topic at hand compared to what one sees elsewhere on the internet).
I could also criticise the "everyone else is lying to you, but we'll tell you the truth" undertone of the video. None of this is particularly new or obscure scientific knowledge. But there may still be plenty of random laypeople saying otherwise (and also plenty of people trying to exploit this misconception for profit by selling you pseudoscientific weight-loss nonsense or some such).