Thanks for the biology! It's a thing that never really caught my interest in school, and probably my weakest area of understanding.
The core thing about Keto that you kinda got wrong is that it is primarily leafy greens - like, 70% of your diet - and the rest is fats and proteins in various forms. Like the Adkins Diet, you eat a "palm-sized" bit of protein with a big ole salad that dwarfs the protein.
So it is basically a heavy-plants diet, but fortifies that with specific proteins, and no carbs.
The interesting part about the low carbs, is that plants store their energy as sugars (carbs) in their roots. So in Keto the shorthand is to eat "above-ground vegetables; mostly the leaves".
It's a little weird to get used to, but, in essence, you have a steak salad as much as possible: a bed of fresh spinach with crunchies like celery and cucumber and onions, with slices of really nice flank steak on top, and a light vinaigrette dressing. (Which, to me, is pretty much a meal I would eat every day, for every meal, as often as I could! :-)
Over the years I have been doing it, I have tweaked and adjusted it according to my body's particular needs, and I would no longer call food intake "Keto", the health benefits I have seen from eating this way have been too numerous to count.
Which is, honestly, like DUUUH... of COURSE eating more veggies, fewer sugars, and zero "processed foods" is going to make you healthier.
But the way that worked for me to get to that kind of diet was via the phenomenal weight loss I encountered the first year. 40 pounds lost, and have been kept off for close to 3 years now. Better sleep. Sharper brain and thinking. No afternoon crash. Zero reliance on coffee to get at it, in the morning.
Keto for me was just the path to the healthy diet we all know we should eat. The early rewards kept me diligent, and the long-term effects have kept me thinking the "Keto way" ever since.