That "new higher level way" is leap seconds. The concept of leap seconds allows us to do date and time calculations in "calendar seconds", and not care about the discrepancy between physical seconds and calendar seconds.

Leap seconds basically add a corrective jump to physical time (what is measured by our super accurate clocks that use physical seconds and not calendar seconds) to match calendar time.

Leap seconds matter if you're doing some scientific or engineering calculation (astronomy, aerospace or whatever) and you need an exact physical time down the fraction of a second between two events that are far apart in the calendar.

They do not enter into everyday calculations, like using time_t seconds to calculate the number of days between two dates.