In order use a captured string as part of a regex match, you need to use a backslash in front of the digit, not a dollar sign:

m/<blank\s+title\s*=\s*(["'])?(.*?)\1\s*>/
                                   --
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To show a simpler example, consider:

$_ = "here are ::framed words:: to capture";

if ( /(::)(.*?)\1/ ) {
    print "text framed by $1 was <$2>\n";
}
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If you try it with $ instead of \, it doesn't work.