Postgres 12

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CREATE TABLE tab ( columnsettings JSONB );

INSERT INTO tab VALUES 
 ('[
    {
        "data": "id",
        "width": 25
    },
    {
        "data": "field_1",
        "width": 125
    },
    {
        "data": "field_3",
        "width": 183
    },
    {
        "data": "field_11",
        "width": 125
    }
]')

CREATE TABLE



INSERT 0 1


UPDATE tab
   SET columnsettings =
   (
    SELECT JSONB_AGG(CASE WHEN j ->> 'data' = 'field_1' THEN 
                               JSONB_SET(j, '{data}', '"newvalue"')
                          ELSE
                               j
                           END)    
      FROM JSONB_ARRAY_ELEMENTS(columnsettings) AS j
   )

UPDATE 1


SELECT JSONB_PRETTY(columnsettings)
  FROM tab


jsonb_pretty


[
    {
        "data": "id",
        "width": 25
    },
    {
        "data": "newvalue",
        "width": 125
    },
    {
        "data": "field_3",
        "width": 183
    },
    {
        "data": "field_11",
        "width": 125
    }
]



SELECT 1