So, why not prepend the key to the list in the first loop instead:

#!/usr/bin/env perl
use strict;
use warnings;

my %seen;

$/ = "";
while (<>) {
    chomp;
    my ($key, $value) = split ('\t', $_);

    my @lines = split /\n/, $key;
    my $key1 = $lines[1];

    $seen{$key1} //= [ $key ];
    push (@{$seen{$key1}}, $value);
}

foreach my $key1 (sort keys %seen) {
    print join ("\t", @{$seen{$key1}});
}
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If this doesn't do it for you then perhaps you might state what grander problem it is that you are trying to solve and a better overall approach might be in order.