Diesel does have a load of additives in it, but the stuff about supermarket diesel is nonsense, all fuel is refined in the same refineries, it doesn't matter which brand you use, the fuel in a particular area will have come from the refinery that is closest to where you buy it
ATF or even engine oil can help with lubricity (a ridiculous made up word) modern low sulphur diesels do not have the lubrication of older fuels, so you can have injector problems as a result, but be careful what you put in, oils have additives too and some of them can damage the fuel system :idea:
The best thing to use is the Lucas upper cylinder lubricant and injector cleaner
https://wheelstips.com/best-diesel-injector-cleaner although even that is unnecessary, injectors will go a million miles without it. Some people will of course swear by their additives, saying they've used them from day one and not had a problem, it's kind of like putting a notice on your fridge saying that no elephants are allowed inside, you can guarantee that it will work, but I don't have a notice on my fridge, yet I've never had an elephant in it, maybe I'm just lucky :lol:
Any other additives that promise increased mpg are pure snake oil, especially ones that can also be added to the crankcase to protect your engine or the oil in it. The only way to improve fuel mileage from the diesel is to improve its BTU content and diesel is one of the most efficient substance on the planet for BTU content, for any product to work it would need to have a better BTU value than diesel and cost less than diesel, none of them do, so you may as well save your money and just buy diesel in the first place