EXISTS by itself vs SELECT EXISTS much slower in query.

[Jimmy A <jimmypsql@xxxxxxxxx>]

A description of what you are trying to achieve and what results you expect.:
I have two equivalent queries, one with an EXISTS clause by itself and one wrapped in a (SELECT EXISTS) and the "naked" exists is much slower.
I would expect both to be the same speed / have same execution plan.

-- slow
explain (analyze, buffers)
SELECT
    parent.*,
    EXISTS (SELECT * FROM child WHERE child.parent_id=parent.parent_id) AS child_exists
FROM parent
ORDER BY parent_id LIMIT 10;

-- fast
explain (analyze, buffers)
SELECT
    parent.*,
    (SELECT EXISTS (SELECT * FROM child WHERE child.parent_id=parent.parent_id)) AS child_exists
FROM parent
ORDER BY parent_id LIMIT 10;

-- slow
https://explain.depesz.com/s/DzcK

-- fast
https://explain.depesz.com/s/EftS

Setup:
CREATE TABLE parent(parent_id BIGSERIAL PRIMARY KEY, name text);
CREATE TABLE child(child_id BIGSERIAL PRIMARY KEY, parent_id bigint references parent(parent_id), name text);

-- random name and sequential primary key for 100 thousand parents.
INSERT INTO parent
    SELECT
        nextval('parent_parent_id_seq'),
        md5(random()::text)
    FROM generate_series(1, 100000);

-- 1 million children.
-- set every odd id parent to have children. even id parent gets none.
INSERT INTO child
    SELECT
           nextval('child_child_id_seq'),
           ((generate_series/2*2) % 100000)::bigint + 1,
           md5(random()::text)
    FROM generate_series(1, 1000000);

CREATE INDEX ON child(parent_id);
VACUUM ANALYZE parent, child;

Both queries return the same results - I have taken a md5 of both queries without the LIMIT clause to confirm.
Tables have been vacuumed and analyzed.
No other queries are being executed.
Reproducible with LIMIT 1 or LIMIT 100 or LIMIT 500.
Changing work_mem makes no difference.

-[ RECORD 1 ]--+---------
relname        | parent
relpages       | 935
reltuples      | 100000
relallvisible  | 935
relkind        | r
relnatts       | 2
relhassubclass | f
reloptions     |
pg_table_size  | 7700480
-[ RECORD 2 ]--+---------
relname        | child
relpages       | 10310
reltuples      | 1e+06
relallvisible  | 10310
relkind        | r
relnatts       | 3
relhassubclass | f
reloptions     |
pg_table_size  | 84516864

PostgreSQL version number you are running:
PostgreSQL 13.4 on arm-apple-darwin20.5.0, compiled by Apple clang version 12.0.5 (clang-1205.0.22.9), 64-bit

How you installed PostgreSQL:
Using homebrew for mac.
brew install postgres

Changes made to the settings in the postgresql.conf file:  see Server Configuration for a quick way to list them all.
checkpoint_completion_target     | 0.9                  | configuration file
checkpoint_timeout               | 30min                | configuration file
client_encoding                  | UTF8                 | client
cpu_tuple_cost                   | 0.03                 | configuration file
effective_cache_size             | 4GB                  | configuration file
log_directory                    | log                  | configuration file
log_min_duration_statement       | 25ms                 | configuration file
log_statement                    | none                 | configuration file
log_temp_files                   | 0                    | configuration file
log_timezone                     | America/Anchorage    | configuration file
maintenance_work_mem             | 512MB                | configuration file
max_parallel_maintenance_workers | 2                    | configuration file
max_parallel_workers             | 4                    | configuration file
max_parallel_workers_per_gather  | 4                    | configuration file
max_stack_depth                  | 2MB                  | environment variable
max_wal_size                     | 10GB                 | configuration file
max_worker_processes             | 4                    | configuration file
min_wal_size                     | 80MB                 | configuration file
random_page_cost                 | 1.1                  | configuration file
shared_buffers                   | 512MB                | configuration file
shared_preload_libraries         | auto_explain         | configuration file
track_io_timing                  | on                   | configuration file
vacuum_cost_limit                | 1000                 | configuration file
wal_buffers                      | 64MB                 | configuration file
wal_compression                  | on                   | configuration file
work_mem                         | 128MB                | configuration file

Operating system and version:
macOS Big Sur 11.2.3
I have confirmed this to happen on ubuntu linux however.

What program you're using to connect to PostgreSQL:
psql

Is there anything relevant or unusual in the PostgreSQL server logs?:
no

Hardware specs:
MacBook Air10,1 M1
8GB RAM
APPLE SSD AP0512Q 500.28GB

Attachment: setup.sql
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