You've got some nested repetition quantifiers there. That can be catastrophic for the performance.
Try something like this:
(?<=")(?:[^"]|"")*(?=")
That can now only consume either two quotes at once... or non-quote characters. The lookbehind and lookahead assert, that the actual match is preceded and followed by a quote.
This also gets you around having to capture anything. Your desired result will simply be the full string you want (without the outer quotes).
I do not assert that the outer quotes are not doubled. Because if they were, there would be no way to distinguish them from an empty string anyway.