The first shop didn't even have one loaf of bread, the second shop also the same story.
From these definitions of 也，found here, I would say the first 也 corresponds with 2. 'even' and the second 也 corresponds with 3. 'also'
It is not surprising that even and also are very close:
even: Old English efen "level," also "equal, like; calm, harmonious; equally; quite, fully; namely,"
also: Old English eallswa "just as, even as, as if, so as, likewise,"
Looks like the same is true of 也
副词，表示同样、并行的意思：你去，我也去。 If you go, I'll go too.
在否定句里表示语气的加强：一点儿也不错。not even slightly wrong
虽然你不说，我也能猜个八九不离十。Although you didn't say, I can also make a good guess.
The etymology of 也 is a bit hard to follow, maybe a wash basin, maybe a funnel, maybe a snake.
Maybe Drooze could enlighten us??
EDIT: carried away with word origins as always, I didn't answer the question!
The sentence is not wrong, just strange
The shop doesn't also doesn't have any bread.
This sounds strange, because, where is the other part of 'also'?
The shop doesn't have any beer and also doesn't have any bread.