if (m/^###|^\s*$/s) {
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should be:

if (m/^###|^\s*\$/s) {
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You need to quote $ because it's the "end of line" match meta character.

It would help to diagnose such problems if you tested your subsequent match and print a diagnostic if it fails:

    unless (m{(^SIP\/2\.0 \d\d\d|^[A-Z]{3,6} ).*(Call-ID: [\S]{25,80})
+[^ ]+: .*}s) {
        print "No match: $_\n";
        next;
    }
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