On the original claim, the LiveStrong.com article titled "Caffeine and Brain Fog" is referenced a primary source backing the claim the claim regarding the energy drink, Celsius's ability to cause brain fog.
After opening the article in another browser, I noticed directly under the title, that its content reported to have been reviewed by Lindsey Elizabeth Cortes (Pfau), MS, RD, CSSD. With a quick google search, I was able to navigate to the "About" page of Rise Up Nutrition LLC, in which Cortes's the founder. On this page, she's credited to have a Bachelor of Science in Nutrition from UMass Amherst, as well as a Master of Science in Sports Nutrition at Florida State University. The biography goes on to share that, "[for] 4 years [Cortes] also worked as the tactical dietitian for Air Force Special Operations and continues to support the US military through various contracts" (Rise Up Nutrition LLC). Therefore, given her previous experience in the field of Science and Nutrition, I feel comfortable that the information included in "Caffeine and Brain Fog" leans more towards accuracy than complete falsehood.
However, after reading the provided LiveStrong.com article on News Detective, I found that its contents focuses primarily on the general effects of caffeine consumption in promoting brain fog, but never mentions the connection to brain fog and Celsius. Curious, I scrolled to the bottom of the piece to the reference section, containing 7 reputable sources such as the Journal of Human Dietetics and the American Psychological Association. However, when I opened all 7 references, and did a key word search for "Celsius," there were zero uses/references across the board.
Finally, I took to Google and searched: "Does the energy drink Celsius cause brain fog?" and cross referenced two of the most reliable sources provided. In both Cleveland Clinic's "Are Energy Drinks Bad for You?" and an article from the NIH titled "Energy Drinks and the Neuropsychological Impact of Caffeine" the previous trend holds true. The general negative effects associated with both basic as well as overconsumption of energy drinks, but again, never mentions Celsius explicitly.
Therefore, I believe instead that the following claim would be true: "Overconsumption of caffeinated beverages have been linked to brain fog." However, in reference to the original claim, I would definitely refer to it as exaggerated and/or misleading.