LEFT JOIN with `json_build_object` returns JSON object initialized with null values, when it should just be null – Postgresql

Suppose the following,

CREATE SCHEMA IF NOT EXISTS my_schema;

CREATE TABLE IF NOT EXISTS my_schema.city (
    id serial PRIMARY KEY,
    city_name VARCHAR(15) NOT NULL
);
CREATE TABLE IF NOT EXISTS my_schema.user (
    id serial PRIMARY KEY,
    city_id BIGINT REFERENCES my_schema.city (id) DEFAULT NULL
);

INSERT INTO my_schema.city VALUES
    (1, 'Toronto'),
    (2, 'Washington');

INSERT INTO my_schema.user VALUES
    (1);

This is my query:

SELECT
  u.id,
  json_build_object(
    'id', c.id,
    'city_name', c.city_name
  ) as city
FROM my_schema.user u
LEFT JOIN my_schema.city c
   ON c.id = u.city_id

The above returns:

[
    {
        "id": 1,
        "city": {
            "id": null,
            "city_name": null
        }
    }
]

I need the following:

[
    {
        "id": 1,
        "city": null
    }
]

I’ve tried using this:

SELECT
  u.id,
  COALESCE(json_build_object(
    'id', c.id,
    'city_name', c.city_name
  ) FILTER (WHERE u.city_id IS NOT NULL), 'none') as city
FROM my_schema.user u
LEFT JOIN my_schema.city c
   ON c.id = u.city_id

But that throws an error. How can I achieve this?