So there's studies that show quality of life is positively correlated to energy consumption.

Without a power grid for an extended period of time, a large number of people would die. Cities, waste, food distribution, water processing, medicine, are all based on access to electricity. Heating is strongly correlated but not necessarily electric.. If electricity stays off permanently people will try to go where their is electricity to help with food, water, medicine. This creates a refugee crisis which likewise strains what resource access there is in those regions. Increasing population suddenly by a small fraction, not a big deal, doubling population in few months nightmare scenario.

Basically the population will long term reflect the food supply. Famines will kill millions.

There are few actual scenarios that would result in lose if the power grid. A solar storm is most likely, but countries that take infrastructure regulation seriously will survive. Those that don't will lose power for month's and focus on bring power back to the most people as quick as possible. Large cities will get power back In a few weeks, and rural areas probably a year or two. Agricultural equipment is mostly Fossil fuel based, so basic food production will function. Food storage and distribution is the problem. The result will be food trucks. Thousands will still die however: medical care will deteriorate one way or another and that means the old and young are more likely to die. The real question will be if electric refugees resort to literally eating the rich in their remote luxury bunkers with backup power.