The claim is that caffeinated drinks, specifically Celsius drinks, causes brain fog. First of all, the title of the claim is misleading because the article that the claim links, never specifically mentions Celsius drinks as causing brain fog, but instead just mentions energy drinks as a whole.
Additionally, while the article mentions that people who suffer from brain fog, and/or chronic fatigue syndrome often turn to coffee or other forms of caffeine to wake them up and make them feel alert, it never explicitly mentions that there is a causal relationship between caffeinated drinks and brain fog itself.
The article uses the credible source Vail Health to support it's definition of what the brain fog condition actually is, but upon taking a closer look at the "causes" section of the study, Dr. Dennis Lipton mentions "...not sleeping well or...high blood sugar" as being common causes of the condition, not Celsius drinks.
However, evidence from the source National Library of Medicine is also used in this article. This source studied caffeine's effects on sleep depending on how many hours before sleeping it was consumed. It found that "caffeine taken 6 hours before bed time has important disruptive effects on sleep."
So, consuming caffeinated drinks can have certain negative effects on the body, such as keeping people awake when they should be sleeping, which can contribute to a feeling of exhaustion, which can contribute to brain fog. But brain fog can also be linked to many other factors as well, such as dehydration or blood pressure spikes from a non-nutritious diet (Lipton). However, caffeine itself is not on this list of direct causes of brain fog, and more specifically, not Celsius drinks.
https://www.vailhealth.org/news/could-it-be-brain-fog
https://pmc.ncbi.nlm.nih.gov/articles/PMC3805807/