readline (aka <>) reads until a newline or eof is encountered before returning. You want sysread since it returns as soon as data is available.

for (;;) {
   my $read = sysread($fh, my $buf, 64*1024);
   die("Can't read from pipe: $!\n") if !defined($read);
   last if !$read;
   print $buf;
}
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