Postgres - Are multi-line statements atomic?

Question

Here's an example:

create database users;
create table users (id int unique);

Then running these together:

insert into users values(1);
insert into users values(1);

I expected the first insert to succeed, but the second to fail. However what I am seeing is that they are run atomically, and no row is inserted. Here are the logs:

2021-11-08 23:04:37.825 UTC [181] LOG:  statement: insert into users values(1);
    insert into users values(1);

2021-11-08 23:04:37.825 UTC [181] ERROR:  duplicate key value violates unique constraint "users_id_key"
2021-11-08 23:04:37.825 UTC [181] DETAIL:  Key (id)=(1) already exists.
2021-11-08 23:04:37.825 UTC [181] STATEMENT:  insert into users values(1);
    insert into users values(1);

What's confusing is that there is no BEGIN; or COMMIT;. Are statements with multiple commands run atomically?

-- EDIT --

I am using Postico client to run these statements.