Timestamptz or timestamp for event times

timestamptz almost always. It stores a point in time in UTC and converts on the way out; timestamp stores a wall clock reading with no idea which wall it was on, which becomes unrecoverable once daylight saving moves.

Split it: add the column nullable, backfill in batches, add a validated check constraint, then set NOT NULL. Each step takes a brief lock instead of one long one, and the backfill can be paused if replication lag grows.