Postgres Jsonb aggregation

You need to break out the arrays with jsonb_to_recordset, rebuild the objects using jsonb_build_object, and aggregate them back up with jsonb_agg

SELECT
  A.City,
  A.JColA,
  B.JColB
FROM (
    SELECT
      City,
      jsonb_agg(JColA) AS JColA
    FROM (
        SELECT
          t.City,
          json_build_object(
            'id', id,
            'name', name,
            'type', type,
            'amount', SUM(amount),
            'full_name', full_name
          ) AS JColA
        FROM YourTable t,
        LATERAL jsonb_to_recordset(t.JColA)
          AS arr(id varchar(10), name varchar(100), type varchar(100), amount decimal (18,2), full_name varchar(100))
        GROUP BY
          t.City, arr.id, arr.name, arr.type, arr.full_name
    ) A
    GROUP BY
      City
) A
JOIN (
    SELECT
      City,
      jsonb_agg(JColB) AS JColB
    FROM (
        SELECT
          t.City,
          json_build_object(
            'key', "key",
            'value', SUM(value)
          ) AS JColB
        FROM YourTable t,
        LATERAL jsonb_to_recordset(t.JColB)
          AS arr("key" varchar(10), value int)
        GROUP BY
          t.City, arr."key"
   ) B
    GROUP BY
      City  
) B ON B.City = A.City;

I feel it's easier to requery the original table again, however if you want to avoid that, you could first aggregate all the arrays together by City, break them back out and re-aggregate.

SELECT
  t.City,
  (
    SELECT
      jsonb_agg(JColA)
    FROM (
        SELECT
          json_build_object(
            'id', id,
            'name', name,
            'type', type,
            'amount', SUM(amount),
            'full_name', full_name
          ) AS JColA
        FROM jsonb_array_elements(t.JColA) AS outerArr,
        LATERAL jsonb_to_recordset(outerArr)
          AS arr(id varchar(10), name varchar(100), type varchar(100), amount decimal (18,2), full_name varchar(100))
        GROUP BY
          arr.id, arr.name, arr.type, arr.full_name
    ) A
  ) AS JColA,
  (
    SELECT
      jsonb_agg(JColB)
    FROM (
        SELECT
          json_build_object(
            'key', "key",
            'value', SUM(arr.value)
          ) AS JColB
        FROM jsonb_array_elements(t.JColB) AS outerArr,
        LATERAL jsonb_to_recordset(outerArr)
          AS arr("key" varchar(10), value int)
        GROUP BY
          arr."key"
     ) B
  ) AS JColB
FROM (
    SELECT
      t.City,
      jsonb_agg(JColA) AS JColA,
      jsonb_agg(JColB) AS JColB
    FROM YourTable t
    GROUP BY
      t.City
) t;

db<>fiddle