The text says: "Comparing a timestamp and timestamptz will always result in false."

That is wrong. Postgres changes the timestamp to timestamptz very quietly in the background. Wether it uses the time zone of the session for this. If it is true or false depends on the TimeZone setting. This is more bad than "always false". In production with UTC it works. On a laptop of a California developer it does not work.

Just tested:

  SET TIME ZONE 'America/Los_Angeles';
  SELECT '2026-03-01 00:00:00'::timestamp = '2026-03-01 00:00:00+00'::timestamptz; /* f   */

  SET TIME ZONE 'UTC';
  SELECT '2026-03-01 00:00:00'::timestamp = '2026-03-01 00:00:00+00'::timestamptz; /* t  */

If you can, use Postgres 16. The double AT TIME ZONE 'UTC' thing from the text is not needed there. There you have date_add with a time zone as the third argument:

date_add(b.month_start, interval '1 month', 'UTC')

This adds the month in UTC and it stays a timestamptz.