There is no significant inflation measure that does not include food.

I agree they're not the entirety of the basket, but they are a core component.

There is no "general price level".

Food and Beverages make up 15% of the US CPI basket. Some other major components are Housing (42%) and Transport (15%).

Here's the full list, which make up the "general price level": https://www.bls.gov/cpi/tables/relative-importance/2020.htm If you believe food is underweighted, then what category do you believe is overweighted?

There is a "general price level", it's just the price level of a sufficiently broad basket.

It is the inflation for the poorest population. What does it matter that 4k tv's are cheaper to people who spend all their money on necessities.

Call it a price rise. But it's not inflation. You don't get to re-define what economic concepts mean.

Would it not be fair to say that different subpopulations experience different effective inflation rates because they buy different things?

Seriously, would it? I’m not an economist. I am aware of RPI/CPI, and inflation is measured independently in different countries within the Eurozone, so it’s not like we can’t have multiple measures for different purposes or populations.

The concept of inflation is an attempt to measure price increases that are due to general monetary factors, as opposed to price increases that are due to market forces in specific industries. It’s fair to try and measure the practical household budget of a typical family, and many governments do, but calling this measurement “inflation” tends to mislead people into thinking that any increase must be because there’s an oversupply of money.

>Would it not be fair to say that different subpopulations experience different effective inflation rates because they buy different things?

Inflation is measured based on the changing the value of a dollar. So no, you can't have different inflation for different people.

You can have a separate idea of a poverty line or cost of living. But that's a different concept and would need different measures.

You can definitely say that the cost of living has risen at different rates for different subpopulations, but you can't say they have experienced different rates of inflation. Inflation is change in the general price level of the economy, and an economy is something that we can study at a macroeconomic level. In this sense, unless you regard a social group as being an economy on its own, with its own GDP, balance of payments, and whole set of macroeconomic variables, we can't speak of it as experiencing a particular inflation rate.