Apart from the mistake BrowserUk pointed out, there are two more:

• you use overload in package main, so oo_test doesn't have overload included - instead overload binds '""' to main::stringify, which doesn't exist
• to properly invoke the overloaded function, you should print "$test", not invoke stringify as method upon $test

#!/usr/bin/perl
use v5.22;
use Data::Dumper;

package oo_test{
    use overload '""' => 'stringify';
    
    sub new{
        my $class = shift;
        my $self = {};
        bless $self, $class;
        return $self;
    }
    
    sub getter{
        my $self = shift;
        while( my $line = <main::DATA> ){
        print $line;
            chomp $line;
            $self->{$.} = $line;
        }
        return $self;
    }
    
    sub stringify{
        my $self = shift;
        return join(" ", values %$self );
    }
};

package main;
my $test = oo_test->new();
$test->getter();
print "$test\n";


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