Get Id from a conditional INSERT

Question

For a table like this one:

CREATE TABLE Users(
    id SERIAL PRIMARY KEY,
    name TEXT UNIQUE
);

What would be the correct one-

Answer 1

For a single row insert and no update:

with i as (
    insert into users (name)
    select 'the name'
    where not exists (
        select 1
        from users
        where name = 'the name'
    )
    returning id
)
select id
from users
where name = 'the name'

union all

select id from i

The manual about the primary and the with subqueries parts:

The primary query and the WITH queries are all (notionally) executed at the same time

Although that sounds to me "same snapshot" I'm not sure since I don't know what notionally means in that context.

But there is also:

The sub-statements in WITH are executed concurrently with each other and with the main query. Therefore, when using data-modifying statements in WITH, the order in which the specified updates actually happen is unpredictable. All the statements are executed with the same snapshot

If I understand correctly that same snapshot bit prevents a race condition. But again I'm not sure if by all the statements it refers only to the statements in the with subqueries excluding the main query. To avoid any doubt move the select in the previous query to a with subquery:

with s as (
    select id
    from users
    where name = 'the name'
), i as (
    insert into users (name)
    select 'the name'
    where not exists (select 1 from s)
    returning id
)
select id from s
union all
select id from i