What's even crazier is that writing plain TIMESTAMP gets you TIMESTAMP WITHOUT TIME ZONE, as is also mandated by the standard (the Postgres docs call this one out specifically). And that behaviour can be summarized as: not only don't store the timezone, but also ignore the timezone you get given.
For example, I'm on GMT/UTC right now, and I see this:
select '2025-01-30T12:00:00-0800'::timestamp with time zone; -- 2025-01-30 20:00:00+00
select '2025-01-30T12:00:00-0800'::timestamp; -- 2025-01-30 12:00:00