"replaced with an empty string" vs "replaced with the empty string" - which is correct?

Give or take, the statement

there can be only one empty string, that is ""

could be considered true. It just depends on how deep you want to take that question (what about a variable of string type with a value of null or nil, does a char variable of '' count as equivalent to a string variable ""? (JavaScript would consider this == vs ===, but I digress))

And for the scope of the question, we will treat that statement as true, which would allude to the usage of "the" rather than "an," since "there can only be one."

But, consider

var str1 = "";
var str2 = "";

There is now more than one empty string, as the empty string is stored in two separate variables, or two separate strings, and therefore there exists two strings at different addresses in the computer's memory, both of which are empty.

So I think "an empty string" is more widely used because you're alluding to the possible existence of more than one string, rather than the existence of more than one empty-string. It wouldn't matter if you used str1 or str2 because they are both empty strings. That's why most people use "an empty string."

But "more widely used" doesn't mean "the only correct way"; use what seems more correct to you, and just know that both ways are fine.