MariaDB 10.3

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CREATE TABLE datawork (id int auto_increment primary key,
                       BcDJSON TEXT);
INSERT INTO datawork (BcDJSON) values 
('{"placards":
     [
     {"barcode":"123 ","destination":"a","weight":"1"}, 
     {"barcode":"456","destination":"b","weight":"2"}
    ]
}'),
('{"placards":
     [
     {"barcode":" 789","destination":"a","weight":"1"}, 
     {"barcode":" 123 ","destination":"b","weight":"2"}
    ]
}');
SELECT BcDJSON FROM datawork


BcDJSON


{"placards":
     [
     {"barcode":"123 ","destination":"a","weight":"1"}, 
     {"barcode":"456","destination":"b","weight":"2"}
    ]
}

{"placards":
     [
     {"barcode":" 789","destination":"a","weight":"1"}, 
     {"barcode":" 123 ","destination":"b","weight":"2"}
    ]
}


UPDATE datawork 
SET BcDJSON = REGEXP_REPLACE(BcDJSON, '"barcode"\\s*:\\s*"\\s*([^ "]+)\\s*"', '"barcode":"\\1"')
SELECT BcDJSON FROM datawork


BcDJSON


{"placards":
     [
     {"barcode":"123","destination":"a","weight":"1"}, 
     {"barcode":"456","destination":"b","weight":"2"}
    ]
}

{"placards":
     [
     {"barcode":"789","destination":"a","weight":"1"}, 
     {"barcode":"123","destination":"b","weight":"2"}
    ]
}