My brain hurts from trying to figure out where the status quo lies, but my
best estimate is that time_t counts in 86400-second days, with zero
corresponding to the epoch date mentioned above. Thus it is neither properly
UTC nor UT1 (it has a UTC epoch and UT1 seconds).
The easiest way to describe this, in lay terms, is that
the OS assumes there are no such things as leap seconds, and deals with
leap seconds in the same way as it does with other clock adjustments:
"Oh, I'm one second late? Let me adjust my clock to be on time again."
If you computer is connected to some NTP server, that happens automatically.
When you know about the next leap second, please tell us, we might all be able to watch :-).