Update all values for given key nested in JSON array of objects
First cte unnest all elements of the array, second one update each element and then simply update the original table building the array again.

with ct as
(
    select id, jsonb_array_elements(data) dt
    from   t
)
, ct2 as
(
  select id, jsonb_set(dt, '{updatedAt}', '"1571150000"', false) dt2
  from   ct
)
update t
set    data = (select jsonb_agg(dt2) from ct2 where ct2.id = t.id);





select * from t;



id | data                                                                                                                                
-: | :-----------------------------------------------------------------------------------------------------------------------------------
 1 | [{&quot;id&quot;: &quot;1&quot;, &quot;status&quot;: &quot;test status1&quot;, &quot;updatedAt&quot;: &quot;1571150000&quot;}, {&quot;id&quot;: &quot;2&quot;, &quot;status&quot;: &quot;test status2&quot;, &quot;updatedAt&quot;: &quot;1571150000&quot;}]



db&lt;>fiddle here