Hm. May some other variants help? Or are they way slower?....
"\G \s*? ^ \s*" # non-greedy
"\G (?= \s* ^ ) \s*" # look-ahead
Upd. And do they reproduce regression?

Upd. May that factoring out of "\s* ^ \s*" help?

    {
        last if $text =~ /\G \s* \Z/gcmsx;

        if     ($text =~ /\G \s* ^ \s*/gcmsx) {
            if     ($text =~ /\G module \s+ (\S+?) \s* \( \s* (.*?) \s
+* \) \s* ;/gcmsx) { $name = $1 }
            elsif  ($text =~ /\G endmodule        /gcmsx) { }
            elsif  ($text =~ /\G \S+ \s+ .*? \s* ;/gcmsx) { }
            else { die "ERROR: unknown syntax\n" }
        } 
        else { die "ERROR: unknown syntax\n" }

        redo;
    }
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