• $tmp_buffer =~ /^<CASE-STUDY/ doesn't match. /m is needed to make "^" match at the start of a line.
• The last regex pattern doesn't match because </CASE-STUDY></INSERT-TOPIC> doesn't exist in the input. There's a newline between the two tags.
• You don't include the last substitution in your last print.

if ($tmp_buffer =~ /^<CASE-STUDY/mi) {
                                 ^
                                 |

   $tmp_buffer =~ /<CASE-STUDY[^>]*><TOPIC-INFO><TITLE>([^<]*)<\/TITLE
+>/i;
   my($xtitle) = $1;
   $tmp_buffer =~ s/<CASE-STUDY([^>]*)>/<TOPIC ID="" HEADING-LEVEL="1"
+><TOPIC-INFO><TITLE>$xtitle<\/TITLE><\/TOPIC-INFO><CASE-STUDY$1>/i;
   $tmp_buffer =~ s/(<CASE-STUDY.*?<\/CASE-STUDY>)\s*<\/INSERT-TOPIC>/
+$1<\/TOPIC>/si;
                                                  ^^^
                                                  |||
   print "debug - $tmp_buffer\n";
                  ^^^^^^^^^^^
                  |||||||||||
}
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