Hashes don't interpolate within quoted strings. You need to do something like this instead:

foreach my $last_name ( keys %people ) {
    print "Last name is $last_name.\n\tDetails are:\n";
    print map { "$_: " . $people->{$last_name}{$_} . "\n\t" }
       keys %{$people->{$last_name}};
    print "\n";
}
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That's untested, so you may have to tinker with it to get your exact desired output, but it should help.