You are printing $string which contains only "a". If you want to print the match, store it for printing later:

if (my ($match) = /(\Q$string\E\S*)/) {
    print "Matched '$string' in '$match'.\n";
}
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Note that

my $content =~ m/.../g;
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is not doing what you think. By adding my, you make $content undefined, so matching it against anything non-empty returns false. You should use warnings which would tell you:

Use of uninitialized value $content in pattern match (m//)