What is the purpose of the parenthesis in this switch and case label?

It is a capability of pattern matching that was introduced in C# 8. { } matches any non-null value. n is used to declare a variable that will hold matched value. Here is a sample from MSDN that shows usage of { }.

Explanation of your sample:

switch (itemsList.Count())
    case 0:
        throw new Exception("No items with that model");

    case 1:
        return itemsList;

    // If itemsList.Count() != 0 && itemsList.Count() != 1 then it will
    // be checked against this case statement.
    // Because itemsList.Count() is a non-null value, then its value will
    // be assigned to n and then a condition agaist n will be checked.
    // If condition aginst n returns true, then this case statement is
    // considered satisfied and its body will be executed.
    case { } n when n > 1:
        return itemsList;

It is known as property pattern. The {} deals with remaining nonnull objects. Property patterns express a property that needs to have a specific constant value. But, in your example, I think it is just to use n in the switch-expression by assuring n is not null. I mean its equivalent is as follows.

if (itemsList is {} n && n.Count() > 1)
    return itemsList;



C# 8.0