A regex should be between / / marks ...

The  =~ operator is sufficiently DWIMic that it will take any string as a regex. It will even take all the  qr// regex modifiers if they are embedded as  (?adlupimsx-imsx) extended patterns.

c:\@Work\Perl>perl -wMstrict -le
"my $regex = '(?xms) ((.) \2{2,})';
 ;;
 for my $s (qw(aeiou aeeiou aeiiiou aeioooou)) {
   print qq{match: captured '$1'} if $s =~ $regex;
   }
"
match: captured 'iii'
match: captured 'oooo'
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... but that won't work ...

The first comment I made is actually rather trivial in the face of your second point; the substitution  s/\),\(/\)\n\(/ is, indeed, a substitution and not a regex — and bang, the whole endeavor hits a brick wall.