extra_float_digits not working as expected when querying table in Redshift

Question

In Redshift, I've created a table with Real column following this example from the docs. When querying Redshift with the Web UI or DbBeaver, I get back [{ realCol: 12345.123 }] where it seems like they are setting extra_float_digits to 2, to get more than the documented 6 significant digits.

When using psql or node-postgres, I always get back the result [{ realcol: 12345.1 }] regardless of what I try to do to set the extra_float_digits flag. I've tried both as a startup parameter, as well running a query to set it. I know redshift is at least recognizing it as if I set it to a value outside the accepted value, it throws an error about an invalid value. At this point I'm at my wits end on how this flag is supposed to work.

I'm using the following code to connect to a Redshift instance using the node-postgres library:

import pg from 'pg';

class CustomClient extends pg.Client {
  getStartupConf() {
    return Object.assign(
      super.getStartupConf(),
      {
        extra_float_digits: '2',
      }
    );
  }
}
const client = new CustomClient({
  // redacted credentials
});

(async function() {
  await client.connect();
  await client.query('SET extra_float_digits = 2');
  const result = await client.query('SELECT * FROM real1;');
  console.log(result.rows);
})().then(() => {
  process.exit();
}).catch((err) => {
  console.error(err);
});

I also tried the following in psql:

psql (14.2, server 8.0.2)
SSL connection (protocol: TLSv1.2, cipher: ECDHE-RSA-AES256-GCM-SHA384, bits: 256, compression: off)
Type "help" for help.

test=# SET extra_float_digits = 3;
ERROR:  3 is outside the valid range for parameter "extra_float_digits" (-15 .. 2)
popsql=# SET extra_float_digits = 2;
SET
popsql=# SHOW ALL;
           name            |    setting
---------------------------+---------------
 analyze_threshold_percent | 10
 datestyle                 | ISO, MDY
 extra_float_digits        | 2
 query_group               | default
 search_path               | $user, public
 statement_timeout         | 0
 wlm_query_slot_count      | 1
(7 rows)

test=# SELECT * FROM real1;
   realcol
-------------
     12345.1
(6 rows)

For both, I would expect the result to be [{ realCol: '12345.123' }], but I cannot get it to work.