MySQL 8.0

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CREATE TABLE YourTable
(
   id int
   , user_json JSON
)
INSERT INTO YourTable (id, user_json)
VALUES
(4783, '{"user": {"firstName": "Joe","lastName":"Rizzo"},"city":"Salisbury"}' )
, (1111, '{"user": {"firstName": "Joe","lastName":"Rizzo"},"city":"Salisbury"}' )
;

Records: 2  Duplicates: 0  Warnings: 0


UPDATE YourTable  
SET    user_json = JSON_INSERT(user_json, '$.user.emailAddress', 'joeR@gmail.com')
WHERE  id = 4783

Rows matched: 1  Changed: 1  Warnings: 0


SELECT CAST(user_json AS CHAR)
FROM   YourTable;


CAST(user_json AS CHAR)


{"city": "Salisbury", "user": {"lastName": "Rizzo", "firstName": "Joe", "emailAddress": "joeR@gmail.com"}}

{"city": "Salisbury", "user": {"lastName": "Rizzo", "firstName": "Joe"}}