Stop using StorageArea.set directly with complex types

[KL13NT]

As documented on the MDN page:

It's generally not possible to store other types, such as Function, Date, RegExp, Set, Map, ArrayBuffer, and so on. Some of these unsupported types will restore as an empty object, and some cause set() to throw an error. The exact behavior here is browser-specific.

The behavior on Firefox, luckily enough, stores Date as strings, but we need to serialize before updating data.