$str =~ /(?:(?|(?:\")(?:[^\\\"]*(?:\\.[^\\\"]*)*)(?:\")))/;

It's missing the capture group that I added: /($RE{delimited}{-delim=>'"'})/

I don't quite understand...

I do basically this:

use Regexp::Common qw/delimited/;

print $RE{delimited}{-delim=>'"'};
[download]

And take what is printed.

How can I get to a pure regex that works then?

The regex is:

(?:(?|(?:\")(?:[^\\\"]*(?:\\.[^\\\"]*)*)(?:\")))
[download]

which contains no capturing groups, hence $1 isn't populated. In my first bit of code, in the regex I added an extra set of parentheses, /($RE{delimited}{-delim=>'"'})/, so there is a capturing group there. That's the equivalent of:

((?:(?|(?:\")(?:[^\\\"]*(?:\\.[^\\\"]*)*)(?:\"))))
[download]

Alternatively, you can take the first regex above and just change the non-capturing group (?:...) that surrounds the entire expression into a capturing group:

((?|(?:\")(?:[^\\\"]*(?:\\.[^\\\"]*)*)(?:\")))
[download]

Or, since you said you wanted to capture the stuff between the quotes, change that non-capturing group into a capturing one:

(?:(?|(?:\")([^\\\"]*(?:\\.[^\\\"]*)*)(?:\")))
[download]

Plus, there's a bunch of simplifications that could be made to the first regex above anyway (really just removing unnecessary groups):

/ \" [^\\\"]* (?: \\. [^\\\"]* )* \" /x
[download]

and just add capturing groups to that as needed.