The claim that Drinking water can cause over hydration which can affect your brain, muscles, and heart, is somewhat true. The condition is called Hyponatremia but it is very rare and is not caused just by drinking water but the overconsumption of it. Through research I have found that there are many reliable sources that can back up this claim.
For primary sources, The NIH did a case study on water intoxication where a 22 year old man slipped into a coma after ingesting 6 liters of water of a 3 hour period. The consumption of that much water in that short of time affected his brain and caused this reaction to occur. (https://pubmed.ncbi.nlm.nih.gov/24570685/)
For secondary sources I found this article from the Mayo Clinic where it describes the symptoms of Hyponatremia. It mentions that it can cause muscle spasms, weakness, cramping, heart, kidney, and liver problems. (https://www.mayoclinic.org/diseases-conditions/hyponatremia/symptoms-causes/syc-20373711)
The potential biases from my primary source would be because they show an extreme case as an example for medical conditions. For my secondary source there would not be bias but they lean towards highlighting what you should do to stay healthy.
My evidence comes from real clinical cases that occurred that show what overconsumption of water can do to the brain, muscles, and heart. It can be undermined by the fact that it is a very rare medical condition that does not occur on an everyday basis. I have not gotten a response from the person who made the original claim.