You can just concatenate the placeholder, like so:

where b ~* ( E'.{2,4}' || ? )
[download]

(here is the test I did:)

sub re {

        
#        $sql = "SELECT a FROM table WHERE b ~* '.{2,4}?' ";
#        $sth = $dbh->prepare($sql);
#        $sth->execute($placeholder);

        my ($dbh) = @_;
        $dbh->do("set search_path to public");
#       $dbh->do("drop table if exists regexjunk;");  -- uncomment if 
+needed
        $dbh->do("create table regexjunk (a text,b text);");
        $dbh->do("
                -- insert 4 rows:
                insert into regexjunk (a,b)
                        values
                                ('one'  , 'FOXxxxxxx')
                            ,   ('two'  , 'xxxxFOXxx')
                            ,   ('three', 'xFOXxxxxx')
                            ,   ('four' , 'xxxxxFOXx')
                        ;
        
        ");

        my $sql = "SELECT a FROM regexjunk WHERE b ~* ( E'.{2,4}' || ?
+ ) ";
        my $sth = $dbh->prepare($sql);
        my $placeholder = 'FOX';
        $sth->execute($placeholder);
        while (my $rrow = $sth->fetchrow_arrayref) {
                print $rrow->[0], "\n";
        }
        -- yields 'two' and 'four' ...
}
[download]