I think the biggest thing here is the hazard ratio
As you say 1.0 is literally nothing. Most say anything below 2.0 shows random chance, and real signals are well over 10.0
I can't be arsed looking up the paper, by chance was its data pulled from FFQ? Ah, I see you mentioned the Nurses study, so that's a yes. Not just a FFQ, but the poster child for the low quality of FFQs
As far as I can tell low carb is fully accepted in psychiatric treatment, fairly accepted in diabetics, proven in weight loss but not widely prescribed, and nearly never used by for profit weight loss organisations because it's so easy to DIY without any special products
Researchers have also noticed that they can get a thousand zero carb eaters from Reddit with high adherence to animal sourced food only, and likewise vegans and vegetarians since we separate ourselves so well, so some good epidemiological research is possible where you can actually compare some hundreds of people who eat only meat to others who eat only plants
It would probably be fairly straightforward to compare the spectrum from vegan through vegetarian, pescatarian, SAD, keto, ketovore, carnivore and all the shades of grey I missed though we're probably unique in our ability to say exactly what we ate every day for years