Good that this question has been asked even with all the flaws that this kind of thing always has.
Just got to the abstract and results and it strikes me that there's an obvious issue with the Gwyneth Paltrow confounder i.e. if you eat a plant based diet you are also likely to have many other healthy habits and may also be fairly middle class. Not saying that LCHF isn't fashionable but if we think about reasons why people do it then we might understand why those people could already be more vulnerable to severity of Covid infection such as they are already overweight or pre diabetic?
Also this is a working age population exposed to Covid (good for the study's purpose) but we now the risk is very age stratified so I'd be looking a the diet and lifestyle of the over 60s possibly with a control and intervention group to see if flu can be prevented or its' severity reduced if we improve immunity say by lifestyle in nursing homes.