I’m on keto for a week (without any effect btw) and eat tons of cheese
I found this out within the first few days because I bought a ketone and glucose blood meter and test strips (from Keto Mojo https://keto-mojo.com/ they ship to EU too) and saw that with my initial keto diet my glucose ketone index (GKI) wasn’t low enough and I was only in low to moderate ketosis. I adjusted my diet and once I got deep enough suddenly it was like the light switch on and my metabolism was working again and my ME symptoms drastically improved.
You cannot eat a lot of vegetables on keto, and you also cannot eat many types of vegetables. You also cannot have too much protein as your liver will convert excess protein into glucose via gluconeogenesis and bring you out of ketosis. I found it takes really careful and restrictive dieting to achieve therapeutic ketosis. I had to use a keto app to input everything I was eating and monitor that I was achieving daily macro goals. Unfortunately it’s really time consuming and a lot of work to do keto.