The liver will start to adapt by performing gluconeogenesis from fat, which has plenty of calories (almost 2x as much per gram as carbohydrates). A human can easily thrive on just fats and protein. See Inuit people who have lived on mostly blubber and meat for centuries.
The ‘everything is sugar’ meme really frustrates the conversation about nutrition and does lead to people making bad nutrition choices, as I’ve personally observed IRL.
Your body can get energy/calories from carbohydrates, fat or protein. Whatever is available. You absolutely need proteins. Between fat and carbohydrates, the body can compensate. There is a clear limit on the ability to process carbohydrates.
Minor nit: essential fatty acids must come from diet as they cannot be synthesized directly. These are alpha-linolenic acid and linoleic acid, with docosahexaenoic acid and gamma-linolenic acid as conditionally essential under some conditions. Though required quantities are minute.
Fat and protein. Humans have several metabolic pathways to convert these into energy, including the production of ketone bodies and gluconeogensis. These are the same metabolic pathways that allow humans to survive off of body fat during a fast. Without these pathways we would literally die within a day or two of not eating[0], since we’re incapable of storing large amounts of glucose from carbohydrates[1].
One can argue that you might be healthier in the long run with carbohydrates, I’m inclined to disagree, but to argue that you can’t get energy without them is just objectively incorrect.
0 - There is a tiny percentage (10 cases) of the population with the inability to build up body fat thanks to the Mardanoid-progeroid-lipodystrophy syndrome. Those with the syndrome can’t store excess calories in the form of body fat, and must eat continuous small meals to meet their metabolic needs. Curiously it seems like the lack of body fat makes their metabolism incredibly inefficient, as they are reported to average 5,000 to 8,000 calories a day. I presume this is because every calorie they eat is “use it or lose it”, resulting in a lot of waste.
1 - Humans can store some glucose in their liver and muscles for immediate use. But strenuous activity can easily exhaust this supply, so it’s not a reasonable source of energy for even moderate fasts.