time data type question

All;

I am testing a planned change for a table in our db - PostgreSQL 14

I created a table like this:

create table alter_test4 (id int, active_ts timestamp without time zone,
active_time time without time zone);

I set my current timezone is set to Central Time:

postgres=# set timezone = 'US/Central';
SET

Then I inserted some rows:
postgres=# insert into alter_test4 VALUES (1, now() - interval '14 days'
, now() - interval '1 hours');
INSERT 0 1
postgres=# insert into alter_test4 VALUES (2, now() - interval '4 days'
, now() - interval '7 hours');
INSERT 0 1
postgres=# insert into alter_test4 VALUES (3, now() - interval '1 day' ,
now() - interval '4 hours');
INSERT 0 1

postgres=# select * from alter_test4;
 id |         active_ts          |   active_time
----+----------------------------+-----------------
  1 | 2024-11-22 13:24:20.675575 | 12:24:20.675575
  2 | 2024-12-02 13:24:29.136082 | 06:24:29.136082
  3 | 2024-12-05 13:24:40.346881 | 09:24:40.346881
(3 rows)

Then I altered both the active_ts and the active_time column data types 
to include time zone

postgres=# ALTER TABLE alter_test4 alter column active_ts set data type
timestamp with time zone;
ALTER TABLE
postgres=# ALTER TABLE alter_test4 alter column active_time set data
type time with time zone;
ALTER TABLE

Now a select shows the timezone offset:

postgres=# select * from alter_test4;
 id |           active_ts           |    active_time
----+-------------------------------+--------------------
  1 | 2024-11-22 13:24:20.675575-06 | 12:24:20.675575-06
  2 | 2024-12-02 13:24:29.136082-06 | 06:24:29.136082-06
  3 | 2024-12-05 13:24:40.346881-06 | 09:24:40.346881-06
(3 rows)

However, if I change my timezone and re-run the select only the
timestamp columns reflect the new timezone, the time columns remain the
same:

postgres=# set timezone = 'America/Denver';
SET
postgres=# select * from alter_test4;
 id |           active_ts           |    active_time
----+-------------------------------+--------------------
  1 | 2024-11-22 12:24:20.675575-07 | 12:24:20.675575-06
  2 | 2024-12-02 12:24:29.136082-07 | 06:24:29.136082-06
  3 | 2024-12-05 12:24:40.346881-07 | 09:24:40.346881-06
(3 rows)

I thought I would see the time columns shift to mountain time as well.
am I doing something wrong?

Thanks in advance