Your second sort phase should sort different lists. In order to do that you should sort more than once. Also, please notice that every element of @s1_events is a hashref, and the 'list' element of the hashref is an arrayref, not another hash. Therefore, you can't $a->{list}{date}.
In order to sort each month's list, I would iterate through months, and sort, like:

for(@s1_events){
    @{$_->{list}}=sort {$a->{date}<=>$b->{date}} @{$_->{list}};
}
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Hth..