Doesn't look that bad to me...

#!/usr/bin/perl -l

use strict; # https://perlmonks.org/?node_id=11125762
use warnings;

my $set = Some::Module->new(qw(oops foo bar bat));
print $set->contains('foo');   # true
print $set->contains('FOO');   # true
print $set->contains('Ops');   # false
print $set->after('foo');       # 'bar'
print $set->is_last('bar');     # false
print $set->is_last('BAT');     # true
print $set->is_last('bat');     # true

package Some::Module;

sub new
  {
  my $self = shift;
  bless [ @_ ], ref $self || $self;
  }

sub contains
  {
  my ($self, $item) = @_;
  scalar grep /^\Q$item\E\z/i, @$self;
  }

sub after
  {
  my ($self, $item, %hash) = @_;
  @hash{map lc, @$self} = @$self[1..$#$self];
  $hash{lc $item};
  }

sub is_last
  {
  my ($self, $item) = @_;
  @$self ? $self->[-1] =~ /^\Q$item\E\z/i : 0;
  }
[download]

Outputs:

1
1
0
bar

1
1
[download]

EDIT: fixed some incorrect comments