How to observe plan_cache_mode transition from custom to generic plan?

TL;DR --

1/ My basic prepared statement doesn't seem to start out with a custom plan
(i.e., no parameter symbols in query text).

2/ EXPLAIN EXECUTE of prepared statement doesn't show query text, as the
documentation seems to imply.  Should it?


Apologies if this belongs on -novice.


Details --

I am trying to understand `plan_cache_mode`, related to a report of a
performance problem (resolved by changing `auto` to
`force_custom_plan`).  I do not have access to the server or data in the
report, so I am trying to reproduce a similar situation myself.  I am
using PostgreSQL 12.

My first step is to observe the change in the plan, from custom to
generic, after the first five queries.  I have unsuccessfully tried to
do this with both `EXPLAIN` and the `auto_explain` extension.

I would appreciate help trying to understand what's happening and what
I've misunderstood.

(After I see the plan changing, I'll use more complicated data and
queries to investigate different performance scenarios. Eventually, I'm

The `PREPARE` documentation
(https://www.postgresql.org/docs/12/sql-prepare.html) indicates:

 1/ Regarding `plan_cache_mode`, "... the first five executions are
 done with custom plans ..."

 2/ Regarding `EXPLAIN EXECUTE ...`, "To examine the query plan
 PostgreSQL is using for a prepared statement, use EXPLAIN (...).  If a
 generic plan is in use, it will contain parameter symbols $n, while a
 custom plan will have the supplied parameter values substituted into
 it."


Using psql, I tried preparing and explaining a very basic query: `SELECT
$1 AS data`.

  Note: Wireshark revealed psql uses simple queries (`PREPARE ...`,
  `EXPLAIN EXECUTE ...` are `Q` messages), not the extended protocol
  (i.e., parse, bind, execute).  I mention this because previous list
  posts mention some libpq prepared statement functions do not result in
  the planning heuristic used by `plan_cache_mode`.


Based on the documentation, I expected the first planned query text to
be: `SELECT 10 AS data`, since it should be a custom plan with
substituted values.  However, the query text always contains a parameter
symbol: `SELECT $1 AS data`.


My questions:


1/ Slightly related, the `EXPLAIN EXECUTE(...)` output does not show the
query text, as the documentation seems to suggest it should (so one may
look for parameter symbols).  Why not?

(Although, none of the documented EXPLAIN options mentions query text
display.  So perhaps it never does?)

  ```
  ~# PREPARE one_param AS SELECT $1 AS data;
  ~# EXPLAIN EXECUTE one_param(10);
                    QUERY PLAN
    -------------------------------------------
     Result  (cost=0.00..0.01 rows=1 width=32)
    (1 row)
  ```

2/ The query text was logged by `auto_explain`.  However, it contains a
parameter symbol; why?  Also, why is the logged query a `PREPARE` statement
(as if a new prepared statement is being created), instead of only the
`SELECT ..` which was executed?

  ```
  LOG:  statement: EXPLAIN EXECUTE one_param(10);
  LOG:  duration: 0.000 ms  plan:
        Query Text: PREPARE one_param AS SELECT $1 AS data;
        Result  (cost=0.00..0.01 rows=1 width=32)
          Output: '10'::text
  ```


Let me know if I should post my postgresql.conf and `auto_explain` settings.

Thanks for any advice,
Richard