Are muslims allowed vinegar?

Factual Questions
1

If not, what do they do for pickles? I was just making some tartare sauce when the neighbour’s children knocked on the door, their ball having found its way into my garden. I was going to offer them a taste when I realised that it had pickled gherkins and capers in it, and vinegar is alcohol that’s gone off. And alcohol, is, of course, forbidden.

So, dopers, clue me in before I make a faux pas.

2

The Prophet’s favorite condiments were honey, olive oil, salt, and vinegar.

The Prophet has also called vinegar a “blessed seasoning”

from

3

Vinegar is essentially dilute acetic acid - whatever it started as, it’s not alcohol any more.