If it's say a scheduler for an application, you might have an activity that occurs every x seconds. At a previous job events like that were often scheduled such that x was a different prime number for each task, in order to minimize regular simultaneous executions. A system like that could easily end up with tasks running on a leap-second.

Your example isn’t scheduling in local time but in system time.

In local time would be “my meeting starts at xxx”. Leap seconds schould not be involved there, and neither the system time. The users aren’t going to be glad you’re doing that.

To make sure you covered those edge cases correctly!

The best coverage is not introducing special cases where they aren’t relevant.