Square brackets [...] in a data structure like that is a reference to an array. A list (...) within a data structure like that is pretty meaningless as lists get flattened.

Either of the following two are the correct way of iterating through it:

my $aktData = $aktivitaet->{'activityData'};
foreach my $data (@$aktData) {
   ...
}
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my @aktData = @{ $aktivitaet->{'activityData'} };
foreach my $data (@aktData) {
   ...
}
[download]

Edit: here's an example of why a list (...) within a hashref isn't what you want.

use Data::Dumper;

my $data = {
  "list"    => ( "foo", "bar", "baz" ),
};

print Dumper($data);
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