Expected: Rise: 2022-04-01T06:12:04 Set: 2022-04-01T18:34:16 (Pacific/Auckland)

I am wondering where you're getting these from, since they don't seem to match any information I could find. My results below do match those from timeanddate.com. Even if you fiddle with DateTime::Event::Sunrise's altitude parameter as per "Sun Height" in its documentation, I don't get the same times. For Astro::Coords, the only reference to time zones in its documentation is "A copy of the input argument is created, guaranteeing a UTC representation." - so I figured it's best to just work with UTC inside the module, and only convert to local time zone once one gets the results. I think the slight deviation between the two modules could be because Astro::Coords takes the altitude into account, or some other minor inaccuracy.

use strict;
use warnings;
use Astro::Coords;
use Astro::Telescope;
use DateTime::Event::Sunrise;
use DateTime;

my %params = ( year => 2022, month => 4, day => 1,
    hour => 0, minute => 1, second => 0,
    time_zone => 'Pacific/Auckland' );
my $obsDate = DateTime->new(%params);
$obsDate->set_time_zone('UTC');

my $tel = Astro::Telescope->new('485');
print "Lat=", $tel->lat('d'), " Lon=", $tel->long('d'),
    " Alt=", $tel->alt, "\n";

my $cSun = Astro::Coords->new(planet => 'sun');
$cSun->telescope($tel);
$cSun->datetime($obsDate);

my $sRise = $cSun->rise_time();
my $sSet  = $cSun->set_time();
$sRise->set_time_zone('Pacific/Auckland');
$sSet ->set_time_zone('Pacific/Auckland');

print "Rise: ",$sRise->strftime('%FT%T %Z'),
      " Set: ",$sSet ->strftime('%FT%T %Z'),"\n";

my $sun = DateTime::Event::Sunrise->new( altitude=>-0.833,
    longitude => $tel->long('d'), latitude => $tel->lat('d') );
$obsDate->add(days=>1); # not sure yet why the two modules differ here
my $rise2 = $sun->sunrise_datetime($obsDate);
my $set2  = $sun-> sunset_datetime($obsDate);
$rise2->set_time_zone('Pacific/Auckland');
$set2 ->set_time_zone('Pacific/Auckland');

print "Rise: ",$rise2->strftime('%FT%T %Z'),
      " Set: ",$set2 ->strftime('%FT%T %Z'),"\n";

__END__

Lat=-41.2842368910727 Lon=174.7654 Alt=144.005447541833
Rise: 2022-04-01T07:35:56 NZDT Set: 2022-04-01T19:13:17 NZDT
Rise: 2022-04-01T07:36:11 NZDT Set: 2022-04-01T19:13:42 NZDT
[download]

Update: For Solstice/Equinox, see my script at Re: calculate length of day as function of space at onset of fall.