There are no date, time or datetime types in JSON, so you'll have to serialise it to a string or an int anyway, and then when deserialising you'll need to identify explicitly which values should be parsed as dates.
Well, you could still have a compound object in JSON, that is output by the Temporal API, and which given as input is guaranteed to result in an equal object it was created/serialized from. This compound object must contain all required infos about timezones and such stuff.