So you want to match the string if any of the words on the line match? Did you want to know if "each word matched" or if "any word matched"?

# Any word matched

while (<$words_fh>) {
   my $re = join '|',
            map quotemeta,
            split;
    
   if ( $teststring =~ /($re)/ ) {
      print("$teststring contains $1\n");
   }
}
[download]

# Each word matched

while (<$words_fh>) {
   for my $word ( split ) {
      if ( $teststring =~ /\Q$word/ ) {
         print("$teststring contains $word\n");
      }
   }
}
[download]