I guess I didn't explain why mine works and why the OP's doesn't work with ".+". Compare

while ($str =~ /($re)/g) {
   print("$1\n");
}
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use re 'eval';

$str =~ /
   ($re)
   (?{ print("$1\n"); })
   (?!)
/x;
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Looks similar? But for the same input, they produce different results.

Input:

my $str = 'aabcdabcabce';
my $re  = qr/a[^a]*/;
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Output from /.../g:

a
abcd
abc
abce
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Output from /...(?{ save results })(?!)/:

a
abcd
abc
ab
a
abc
ab
a
abce
abc
ab
a
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/...(?{ save results })(?!)/ is key in finding all possible matches. It forces the regex to try everything to obtain a match.