Postgres now() timestamp doesn’t change, when script works

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From TFM, highlights mine:

9.9.4. Current Date/Time

PostgreSQL provides a number of functions that return values related
to the current date and time. These SQL-standard functions all
return values based on the start time of the current transaction:

CURRENT_DATE
CURRENT_TIME
CURRENT_TIMESTAMP
CURRENT_TIME(precision)
CURRENT_TIMESTAMP(precision)
LOCALTIME
LOCALTIMESTAMP
LOCALTIME(precision)
LOCALTIMESTAMP(precision)

…

Since these functions return the start time of the current
transaction, their values do not change during the transaction. This
is considered a feature: the intent is to allow a single transaction
to have a consistent notion of the “current” time, so that multiple
modifications within the same transaction bear the same time stamp.

PostgreSQL also provides functions that return the start time of the
current statement, as well as the actual current time at the instant
the function is called. The complete list of non-SQL-standard time
functions is:

transaction_timestamp()
statement_timestamp()
clock_timestamp()
timeofday()
now()

transaction_timestamp() is equivalent to CURRENT_TIMESTAMP, but is
named to clearly reflect what it returns. statement_timestamp()
returns the start time of the current statement (more specifically,
the time of receipt of the latest command message from the client).
statement_timestamp() and transaction_timestamp() return the same
value during the first command of a transaction, but might differ
during subsequent commands. clock_timestamp() returns the actual
current time, and therefore its value changes even within a single SQL
command. timeofday() is a historical PostgreSQL function. Like
clock_timestamp(), it returns the actual current time, but as a
formatted text string rather than a timestamp with time zone value.
now() is a traditional PostgreSQL equivalent to transaction_timestamp().

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