BUG #18156: Self-referential foreign key in partitioned table not enforced on deletes

The following bug has been logged on the website:

Bug reference: 18156
Logged by: Matthew Gabeler-Lee
Email address: fastcat(at)gmail(dot)com
PostgreSQL version: 16.0
Operating system: Linux
Description:

When a partitioned table has a self-referential foreign key, I'm finding
that the key is not enforced during deletes from the table.

A simple repro script:

create table x (
p int4 not null,
i int4 not null,
f int4 null,
primary key (p, i),
foreign key (p, f) references x (p, i)
)
partition by list (p);
create table x1 partition of x for values in (0);

insert into x values (0,1,null), (0,2,1);
delete from x where (p,i) = (0,1);
select * from x;

The final select shows the one row with the clearly violated foreign key
values:
p | i | f
---+---+---
0 | 2 | 1
(1 row)

I've reproduced this with 15.4 and 16.0 using the official docker images,
specifically `postgres/15-alpine` and `postgres/16-alpine`. I haven't tested
older versions as my application requires features new to 15.x. I've tried
with both list and hash partitioning, and it reproduces with both. I can
only reproduce it with self-referential foreign keys and only with
partitioned tables.

I discovered this with a slightly more complex situation involving an `on
delete set null` clause in the FK, but as seen above that is not required to
reproduce the issue.