From your problem description, it seems like you simply want:

my $sql3 = "select * from table3";
my $table3 = $dbh->selectall_hashref("foreign_key_table3");
...
foreach (keys(%$table1)) {
  $table1_foreign_key_table3 = 
    $table3->{$table1->{$_}{foreign_key_table3}}{primary_key}
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