Invalid Week number returned

Hello Redshift team,

I am trying to find a way to return the week number as 1 when date is 1st Jan each year. While testing for these years (2000,2005,2010,2011,2012,2016,2017,2021,2022), the value returned for week number is 52, instead of 1 .

-- Query 1 (output 52)  
select extract(week from '2022-01-01'::date);  
select date_part(w, '2022-01-01'::date);

-- Query 2  (output 52)  
select extract(week from '2022-01-02'::date);  
select date_part(w, '2022-01-02'::date);

-- Query 3  (output 2022-01-01)  
-- Query to find the first week for the year 2022  
select to_date(1||' '||2022,'WW YYYY')

Much appreciate if you can please clarify this for me

1. 1st Jan of each year isn't this date supposed to return as week 1 for every calendar year? If not, please let me know what needs to be done.
2. In 'Query 2', the week returned is 52, despite it falls on 2nd Jan 2022 and on the second week of the month. I am quite not sure why its still returning 52 here.
3. With 'Query 3', I see the result shows first week of 2022 as 1st Jan, which is what I am after. I am confused why the 'extract' and 'date_part' functions are returning a different week number, different from the 'to_date' function?

I tried setting the session timezone to UTC, but still the results are same. SET timezone to default;

Cluster details:
Version: 1.0.36224
Region: us-east-1
SQL Client: Redshift Query Editor V2