可以使用jsonb_set：

select col from (
  select col, jsonb_set(col, '{relations}', jsonb_agg(s.relation_updated)) as col_updated
  from (
    select *, jsonb_set(relation::jsonb, '{status}', 
              CASE
                 WHEN relation ->> 'status' = 'Notlive' THEN '"No More"'::jsonb
                 ELSE relation -> 'status'
               END) as relation_updated
    from mytable t,
         jsonb_array_elements(t.col->'relations') as relation
   ) as s
   group by col
) as s

1.使用jsonb_array_elements()提取所有数组元素，并使用jsonb_set()更新数组元素中的状态。CASE子句执行条件检查。
1.使用jsonb_agg将数组元素聚合到一个数组中
update语句可以是：

update mytable t
set col = u.col_updated 
from (
  select col, jsonb_set(col, '{relations}', jsonb_agg(s.relation_updated)) as col_updated
  from (
    select *, jsonb_set(relation::jsonb, '{status}', 
              CASE
                 WHEN relation ->> 'status' = 'Notlive' THEN '"No More"'::jsonb
                 ELSE relation -> 'status'
               END) as relation_updated
    from mytable t,
         jsonb_array_elements(t.col->'relations') as relation
   ) as s
   group by col
) as u
where u.col = t.col

Demo here