Tried a whole bunch of things, not all worked, but currently at about 20X faster on 231MB fake file (perl v5.32.0).

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11128141
use warnings;
use Time::HiRes qw( time );

my $string = do { local(@ARGV, $/) = '50k.foo'; <> };
my $start = time;
parse_v( $string );
printf "seconds %.3f for length %d file\n", time - $start, length $str
+ing;

sub parse_v
  {
  local $_ = shift;
  my $name;
  while( 1 )
    {
    if(/\G (?: (?!endmodule\b|module\b) \S+ \s [^;]* ; |
      (?<!\N) endmodule \b) \s* /gcx) { }
    elsif(/\G (?<!\N) module \s+ (\S+?) \s* \( [^)]* \) \s* ; \s* /gcx
+)
      { $name = $1 }
    else { /\G \z/gcx ? last : die "ERROR: unknown syntax at @{[pos($_
+)]}\n" }
    }
  print "LAST MODULE (Perl $]): $name\n";
  }
[download]

For double negative fans, (?<!\N) means "not preceded by not a newline".