Inserting multiple rows that are related to a parent table using postgresql functions

insert_with_parent_id.sql

-- Schema (redacted)
CREATE TABLE set
(
    workout_id INTEGER,
    kgs NUMERIC NOT NULL,
    reps INTEGER NOT NULL,
    placement INTEGER NOT NULL,
    exercise_id INTEGER,
    CONSTRAINT set_workout_id_fkey FOREIGN KEY (workout_id) REFERENCES workout (id),
    CONSTRAINT set_exercise_id_fkey FOREIGN KEY (exercise_id) REFERENCES exercise (id)
);

CREATE TABLE workout
(
    id INTEGER PRIMARY KEY NOT NULL,
    date DATE DEFAULT ('now'::text)::date,
    client_id INTEGER,
    CONSTRAINT workout_client_id_fkey FOREIGN KEY (client_id) REFERENCES client (id)
);

CREATE TABLE client
(
    id INTEGER PRIMARY KEY NOT NULL,
    nick TEXT,
    email TEXT
);

CREATE TABLE exercise
(
    id INTEGER PRIMARY KEY NOT NULL,
    title TEXT NOT NULL,
    display_name TEXT NOT NULL
);

CREATE OR REPLACE FUNCTION add_new_workout (
  client INTEGER,
  kgs REAL[],
  reps INTEGER[],
  placement INTEGER[],
  exercise_id INTEGER[]
)
  RETURNS VOID AS $$
BEGIN
   WITH new_workout AS (
     INSERT INTO workout (date, client_id) VALUES (now(), client)
     RETURNING workout.id
   )
   INSERT INTO set (workout_id, exercise_id, kgs, reps, placement)
   SELECT id, unnest(exercise_id), unnest(kgs), unnest(reps), unnest(placement)
   FROM new_workout;
END;
  $$ LANGUAGE plpgsql
;

-- Here is how we call the function
-- based on the following data
-- client_id: 1
-- sets:
--  1. kgs: 100, reps: 8, exercise_id: 2
--  2. kgs: 110, reps: 7, exercise_id: 2

SELECT add_new_workout(1, array[100, 110], array[8, 7], array[1,2], array[2, 2]);