How does that number on the package get measured?
When I eat nuts, cashews, etc., did 100% of the food get digested and absorbed? A day later or so, there seems to be counterevidence of that plainly visible in the bathroom.
We are talking about the theory that if you eat fructose, or if you eat 'highly processed foods' there is some complex hormone response that causes those calories to be preferentially stored as fat or to slow the metabolism down so they aren't burned.
For sure you are correct when you say that the calories on the label of a food is just an estimate, and not a very good one.
When people talk about "restricting your caloric intake", they are very obviously talking about what's written on the package and not after making calculations based on whether it's fat, protein or carbohydrates. So I think both issues are very tightly related.
What's the diet you would eat every day to get into a calorie surplus even though you are in >500 calorie deficit according to the labels?
However, you can make the calculations based on the numbers I gave in my other comment - which are taken from Why Calories Don't Count from Dr Giles Yeo.
But this is assuming you calculate your daily calorie burn with one diet that is pure protein and then convert to one that has 100% calorie availability, you still can't overcome 500 calories of deficit on paper!
Realistically you would change diets, then find your baseline based on the new diet, and then calculate a calorie deficit from there. In that case you would be very close to a 500 calorie deficit, and you would unavoidably lose about 1lb of fat per week. A 500 calorie deficit sucks but you will adapt to it in a few months if you stick to it. I've managed to lose over 50lbs in the last year, probably close to 75lbs of fat mass. (I did use a GLP1, dieting is hard)
The cause of a failure to lose weight with moderate calorie restriction is always a failure to maintain the calorie restriction aka cheating on the diet (because it is incredibly hard to do when you aren't used to it).
I lived abroad for a year and, when coming back home, started eating healthily (i.e. more greens and less reds, avoiding added salt). In about 3 months, I managed to reduce my weight by 10% - about 6kg. Although I have to admit, if anything, I wanted to keep those kilograms because it was helping me for weight-training lol. My objective was never to lose weight.