It’s more likely in that instance that the separated cheese came from a botulism infected source. Clostridium botulinum is a obligate anaerobe so it can’t grow in the air we breathe but it can grow in canned food. Can then gets super puffy and if someone doesn’t notice or realize the problem all the toxins go into the food. You can to cook the food at a high temperature for a long time to inactivate it making botulism one of the big food poisoning agents.

The word botulism refers to a disease caused by the botulinum toxin, not to infection by the bacteria itself. In babies infection that then produces the toxin is the bigger risk, but in adults the larger risk is poisoning from food that has been contaminated with botulinum and that has not been stored in such a way to stop the bacteria spores germinating. So you would not have had a gut infection as I've described, you would probably have eaten the cheese and your gut would have killed off the bacteria but absorbed the toxin.

I am interested that it's cheese though! Botulism is usually associated with canned/preserved goods, and it's an anaerobic bacteria, so I wouldn't expect it to like cheese. When you say 'separated,' do you mean curdled/separated into curds and whey? I found this article that shows that dairy with botulinum contamination does curdle (as curdling is a chemical process and not an organic one, many milk contaminants do not cause it): https://pubmed.ncbi.nlm.nih.gov/10456739/