Why does time zone have such a crazy offset-from-UTC on year 0001 in Postgres?
On 18th of November, 1883 at 12:00 (new time), standard time was adopted by the American railroads.
This means that before that time, Los Angeles used actual local time, based on mean solar time. After that, it was moved to its local time zone, which, being an integral offset of hours from the Greenwich Mean Time, was slightly different from the previous time.
Want to know more?

Download the tzdata Timezone Database from IANA: Time zones.

Inside, you'll find the definitions of the (many) timezones, which have lots of variations over time, along with lots of comments detailing what changes where made and when. It's entertaining reading!

Wikipedia has also some interesting facts, in the Wikipedia: Time zone page, regarding the 1883, November 18 change:



Railway time
...
Timekeeping on the American railroads in the mid-19th century was somewhat confused. Each railroad used its own standard time, usually based on the local time of its headquarters or most important terminus, and the railroad's train schedules were published using its own time. Some junctions served by several railroads had a clock for each railroad, each showing a different time.
... Dowd's system was never accepted by American railroads. Instead, U.S. and Canadian railroads implemented a version proposed by William F. Allen, the editor of the Traveler's Official Railway Guide. The borders of its time zones ran through railroad stations, often in major cities. For example, the border between its Eastern and Central time zones ran through Detroit, Buffalo, Pittsburgh, Atlanta, and Charleston. It was inaugurated on Sunday, November 18, 1883, also called &quot;The Day of Two Noons&quot;, when each railroad station clock was reset as standard-time noon was reached within each time zone. The zones were named Intercolonial, Eastern, Central, Mountain, and Pacific. ...

Also note that this is not specific to Postgresql. This is valid for any software or operating system that uses the tzdata database (though of course many will be limited to dates either post 1970 or post 1901, so 1883 is beyond reach, but there are many, many other adjustments all over the place at different times).