How to check the number of rows inserted into the different partitions in a PostgreSQL partitioned table

Create the table:

CREATE TABLE mytable
(
    id bigserial,
    key text COLLATE pg_catalog."default" NOT NULL,
    outdata jsonb,
    partno integer,
    koffset bigint,
    handled_at timestamp with time zone,
    inserted_at timestamp with time zone NOT NULL DEFAULT now(),
    kyear integer NOT NULL, -- Ensure it's NOT NULL to work properly with partitions
    nk boolean NOT NULL,
    CONSTRAINT mytable_pkey PRIMARY KEY (id,kyear)
)
PARTITION BY RANGE (kyear);

Create the partitions. Make it suitable for ranges that adhere to the standard YYYYMM:

CREATE TABLE mytable_202501
PARTITION OF mytable
FOR VALUES FROM (202501) TO (202502);

CREATE TABLE mytable_202502
PARTITION OF mytable
FOR VALUES FROM (202502) TO (202503);

Insert some test values:

INSERT INTO mytable (key, outdata, partno, koffset, handled_at, kyear, nk)
VALUES
    ('A123', '{"data": "test1"}', 101, 500, NOW(), 202501, TRUE),
    ('B456', '{"data": "test2"}', 102, 600, NOW(), 202501, FALSE),
    ('C789', '{"data": "test3"}', 103, 700, NOW(), 202501, TRUE);

INSERT INTO mytable (key, outdata, partno, koffset, handled_at, kyear, nk)
VALUES
    ('D111', '{"data": "test4"}', 104, 800, NOW(), 202502, FALSE),
    ('E222', '{"data": "test5"}', 105, 900, NOW(), 202502, TRUE),
    ('F333', '{"data": "test6"}', 106, 1000, NOW(), 202502, FALSE);

Confirm that the data is indeed there:

select * from mytable;

Finally, verify that the rows have been commited to two different partitions:

musicdb=> SELECT relname, n_tup_ins
musicdb-> FROM pg_stat_all_tables
musicdb-> WHERE relname IN ('mytable_202501', 'mytable_202502');
    relname     | n_tup_ins
----------------+-----------
 mytable_202501 |         3
 mytable_202502 |         3
(2 rows)