"Number of seconds since the unix epoch" describes a physical measurement (that can be related directly to TAI) that would not be affected by leap seconds. You could store that number to allow you to recover TAI timestamps (I'm not aware of any OS that does this, but there's no reason it wouldn't be possible).
Unix time does indeed repeat itself so as to remain in alignment with UTC. But unix time is not the number of seconds since the unix epoch.
Thank you, I think I understand, but disagree on terminology.
Leap seconds are not excluded from number of seconds since Unix epoch, interpreted on a physical, TAI, UTC, typical local time scales.
However, they are indeed excluded from "number of seconds since Unix epoch", when interpreted in unix time. In unix time, those seconds simply don't exists (never happened) and the events of those seconds are smooshed sometime. Unix time representation forms a (quirky) timescale.
I'll quote a few excerpts from 'date' man page of linux, openbsd and for gettimeofday:
Convert seconds since the epoch (1970-01-01 UTC) to a date
Print out (in specified format) the date and time represented by seconds from the Epoch.
The time is expressed in seconds and microseconds since midnight (0 hour), January 1, 1970
Hmm. The first definition I saw of "unix timestamp" explicitly defined it as "86400 * number of days since 1970-01-01 + number of seconds since midnight", which I thought was clever and clear, but I can't find it now. Having looked up the POSIX standard at https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1... it seems you're right and I'm wrong; they define "Seconds Since the Epoch" as "A value that approximates the number of seconds that have elapsed since the Epoch...". In my view this is an extremely poor choice of terminology, because "seconds since the epoch" should have its plain English meaning of the number of SI seconds that have passed since that event; defining some "second" that is almost, but not quite, an SI second seems like a recipe for disaster.
AFAIK, unix time skips a beat or repeats itself to remain in alignment with UTC, and just keeps chugging along.