Well, all time stamps are rounded or floored to the nearest second (or millisecond, or micro, or...) because you only have a finite amount of space to store the

Well, all time stamps are rounded or floored to the nearest second (or millisecond, or micro, or...) because you only have a finite amount of space to store them — you always have infinitely many time stamps mapping to each Unix second. This means you can just adjust the mapping around the leap second. A naive implementation might have those two real-life seconds tick twice as fast to take only one Unix second. Or you could have the whole day’s seconds tick 86401/86400 times as fast, etc. In terms of the mapping from continuous time to discrete time, this is just as fine as the non-leap-second case.