You could use

my $self = $class->Parent::new(...);
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instead of

my $self = $class->SUPER::new(...);
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And you might even have to in some weird situations (although use mro 'c3'; would probably be a better fix).

But using Parent is redundant. You already specified it's the parent class. To use it here is to needlessly hardcode a value. Nothing good can come of that.