Understanding max_locks_per_transaction

We're using PostgreSQL 13.10, installed on CentOS 7 from PGDG RPMs.

Recently we've run into "out of shared memory" issues with a hint at
increasing max_locks_per_transaction. The problem is well described in the
PostgreSQL documentation and various blog posts found around the internet,
and the solution is straightforward - touch fewer objects per transaction
or increase the size of the lock table. The error occurs when joining
partitioned tables, and changing the query structure is something we'd like
to avoid, so we are going the route of increasing the size of the lock
table by increasing max_locks_per_transaction.

Many blog posts suggest against using an arbitrarily large value for
max_locks_per_transaction to avoid excess memory usage by the lock table.
Contrary to that is an email from Tom Lane [1] indicating that a lock table
with several million slots wouldn't be so bad. A SO answer from Laurenz
Albe [2] tells us that a lock entry consumes 168 bytes so a table with 1m
slots would consume somewhere around 160MB (assuming we are on the same
architecture, but if not then at least still probably within an order of
magnitude). I suppose I could set the max_locks_per_transaction value
really high, but, on the other hand, if I can make a pretty good estimate
about how many locks are actually needed then I can set a lower value and
let some of that RAM be used for other things like disk caching instead.
So here I am, trying to estimate the amount of locks that would actually be
needed but have some questions and am running into some behavior that I do
not expect.

Most discussions regarding the lock table say that the size of the lock
table determines how many locks can be held. The documentation for
max_locks_per_transaction [3] reads slightly different though, and in
particular this phrases stands out to me:

> no more than this many distinct objects can be locked at any one time

To me, that seems to be saying that multiple locks for the same object
(e.g. for a single table) would only consume a single lock table entry.
Finally on to my first question: Am I interpreting the documentation
correctly, that multiple locks for the same object only consume a single
lock table entry, or am I reading too much into this and the size of the
lock table really does dictate the total number of locks regardless of
whether those locks point to the same object? If my interpretation is
correct, then I can size the lock table to be slightly above the total
number of database objects and I should be safe.

I tried to test my understanding by creating two database connections and
in each connection issuing a query that touched a large number of tables
(enough to almost reach the size of the lock table). My theory was that if
multiple locks for the same object only consume a single lock table entry,
then multiple connections could each issue the same big query that used a
large number of locks and no issue would arise. For example, with the
default settings (max_connections = 100, max_prepared_statements = 0,
max_locks_per_transaction = 64) I should have a lock table with 6400 slots
so two connections that both touch 6000 database objects should be able to
run concurrently. That test succeeded, but led me to the next
observation...

To my surprise, during my testing I was able to issue queries that used
well above the maximum number of locks that I was expecting and those
queries completed without issue. Below are the relevant database settings
and the results of a statement that locks many objects.

archive=# show max_connections ;
max_connections
-----------------
100
(1 row)
archive=# show max_prepared_transactions ;
max_prepared_transactions
---------------------------
0
(1 row)
archive=# show max_locks_per_transaction ;
max_locks_per_transaction
---------------------------
64
(1 row)
archive=# begin;
BEGIN
archive=*# explain <large select statement that joins many partitions>
<explain output omitted for brevity>
archive=*# select count(*) as total, count(*) filter (where granted) as
granted from pg_locks;
total | granted
-------+---------
7568 | 7568
(1 row)
archive=*# select count(distinct relation) from pg_locks ;
count
-------
7576
(1 row)

According to the documentation, I should have a lock table with 6400
entries but somehow have been able to obtain 7576 locks. So my second and
last question: how is this possible - shouldn't I have received an "out of
shared memory" error since I exceeded 6400 distinct locked objects?

[1] https://www.postgresql.org/message-id/25925.1669420577@sss.pgh.pa.us
[2] https://stackoverflow.com/a/65084207/2934470
[3]
https://www.postgresql.org/docs/current/runtime-config-locks.html#GUC-MAX-LOCKS-PER-TRANSACTION

Craig