BUG #17532: Prepared statements and insert on conflict can fail on the 6th execution

The following bug has been logged on the website:

Bug reference:      17532
Logged by:          Jack Christensen
Email address:      jack@jackchristensen.com
PostgreSQL version: 14.4
Operating system:   MacOS
Description:

A user of the Go driver pgx reported a strange bug
(https://github.com/jackc/pgx/issues/1234). After investigating the issue I
was able to duplicate it in directly in psql. The problem occurs when a
prepared statement has an INSERT ... ON CONFLICT. The statement works the
first 5 times and fails on the 6th time with ERROR:  there is no unique or
exclusion constraint matching the ON CONFLICT specification. I would guess
this has to do with the planner choosing a generic or custom plan.

Here is the reproduction case:

CREATE TYPE promo_reason AS ENUM ('promo_reason');
CREATE TYPE promo_type AS ENUM ('promo_type');

CREATE TABLE promos
(
promo_id    UUID         NOT NULL PRIMARY KEY,
user_id     UUID         NOT NULL,
reason      promo_reason NOT NULL,
type        promo_type   NOT NULL
);

CREATE UNIQUE INDEX promotions_user_id_first_transfer_key ON promos
(user_id)
WHERE type = 'promo_type' AND reason = 'promo_reason';

PREPARE s AS INSERT INTO promos
    (promo_id, user_id, reason, type)
VALUES
    ($1, $2, $3, $4)
ON CONFLICT (user_id) WHERE type = $4 AND reason = $3
DO NOTHING;

EXECUTE s ('00ebd890-f5ac-47c7-9365-4ce9875c04a1',
'132b64e6-1dc9-46cb-9349-5a0d7469622b', 'promo_reason', 'promo_type');
EXECUTE s ('8e3775d9-af90-472f-9720-d0341ff7bba7',
'132b64e6-1dc9-46cb-9349-5a0d7469622b', 'promo_reason', 'promo_type');
EXECUTE s ('f983db27-62d9-4ef1-bc67-e1e492eee48e',
'132b64e6-1dc9-46cb-9349-5a0d7469622b', 'promo_reason', 'promo_type');
EXECUTE s ('10532081-851c-4dc4-9d83-8750bd4cf78d',
'132b64e6-1dc9-46cb-9349-5a0d7469622b', 'promo_reason', 'promo_type');
EXECUTE s ('98e049e4-8762-4c95-be6c-31f4d8f9b04e',
'132b64e6-1dc9-46cb-9349-5a0d7469622b', 'promo_reason', 'promo_type');
EXECUTE s ('355972ac-20a4-4c17-b28d-70d8cb2dd5b8',
'132b64e6-1dc9-46cb-9349-5a0d7469622b', 'promo_reason', 'promo_type');

And here is the output I get when running it:

CREATE TYPE
CREATE TYPE
CREATE TABLE
CREATE INDEX
PREPARE
INSERT 0 1
INSERT 0 0
INSERT 0 0
INSERT 0 0
INSERT 0 0
psql:prepared_statement_vs_on_conflict_bug.sql:27: ERROR:  there is no
unique or exclusion constraint matching the ON CONFLICT specification