https://gaming.stackexchange.com/a/396331/163757 from the game files. See that answer for the details.
I found this larger image, originally sourced from https://www.seekpng.com/ima/u2q8r5r5t4q8o0u2/ . I've circled the words that I was able to make out:
A higher contrast image can be seen https://i.imgur.com/zndsHKt.png .
I'm pretty confident in the following:
Black Circle: Fresh
Red Circle: Drive
Purple Circle: In
Green Circle: Dairy
As for the brown circle, I think it might be either an expiration or packaging date, possibly saying "May 1" and then the rest looks like the letters "LK". I originally though LK might be Roman numerals for the year part of the date, but "K" doesn't exist in Roman numerals. Alternatively, I can also see it saying "May Milk", which perhaps is the "company" that produced and packaged the milk, but no Fallout lore I've found has any reference to this name. https://gaming.stackexchange.com/questions/396274/what-does-the-embossed-text-say-on-the-empty-milk-bottle-in-fallout-4/396278?noredirect=1#comment556500_396278 , it's been said that it looks like "Hay Milk", which in the dairy industry, would denote that the milk came from cows https://en.wikipedia.org/wiki/Haymilk . Some https://gaming.stackexchange.com/questions/396274/what-does-the-embossed-text-say-on-the-empty-milk-bottle-in-fallout-4/396278#comment556514_396278 pointed out "Raw Milk" and this seems to be what the text is https://gaming.stackexchange.com/a/396331/163757
From some research, seems drive-in dairies were kind of like convenience stores of the 1940s and 1950s, which would suit the Fallout time period/theme (prior to the world being destroyed that is). One real life example I found was https://en.wikipedia.org/wiki/Rockview_Farms . Their https://www.rockviewfarms.com/rockview-history/ even shows pictures of what their drive-in dairies were like.
So, "Fresh Drive In Dairy" makes sense to me to be written on the bottle as a slogan of some sort. As for the rest of the words, it's way too small/blurry to make out. The part above the brown circle I can make out a capitalized "A", making me think is could say "Grade A" for https://en.wikipedia.org/wiki/Grade_A_milk .