No unique or exclusion constraint matching the ON CONFLICT

Per the docs,

All table_name unique indexes that, without regard to order, contain exactly the
conflict_target-specified columns/expressions are inferred (chosen) as arbiter
indexes. If an index_predicate is specified, it must, as a further requirement
for inference, satisfy arbiter indexes.

The docs go on to say,

[index_predicate are u]sed to allow inference of partial unique indexes

In an understated way, the docs are saying that when using a partial index and
upserting with ON CONFLICT, the index_predicate must be specified. It is not
inferred for you. I learned this
here, and the following example demonstrates this.

CREATE TABLE test.accounts (
    id int PRIMARY KEY GENERATED BY DEFAULT AS IDENTITY,
    type text,
    person_id int);
CREATE UNIQUE INDEX accounts_note_idx on accounts (type, person_id) WHERE ((type)::text="PersonAccount"::text);
INSERT INTO  test.accounts (type, person_id) VALUES ('PersonAccount', 10);

so that we have:

unutbu=# select * from test.accounts;
+----+---------------+-----------+
| id |     type      | person_id |
+----+---------------+-----------+
|  1 | PersonAccount |        10 |
+----+---------------+-----------+
(1 row)

Without index_predicate we get an error:

INSERT INTO  test.accounts (type, person_id) VALUES ('PersonAccount', 10) ON CONFLICT (type, person_id) DO NOTHING;
-- ERROR:  there is no unique or exclusion constraint matching the ON CONFLICT specification

But if instead you include the index_predicate, WHERE ((type)::text="PersonAccount"::text):

INSERT INTO  test.accounts (type, person_id) VALUES ('PersonAccount', 10)
ON CONFLICT (type, person_id)
WHERE ((type)::text="PersonAccount"::text) DO NOTHING;

then there is no error and DO NOTHING is honored.