Promise.all() throwing error while connecting to database Error: timeout exceeded when used with Node-Postgres

I have Node.js express app with Postgres as a database. I'm using pg for database communication from the app.

This is how my db.service looks like

import { Pool } from 'pg';

const dbConfig = {/*my valid db configuration*/};

const pool = new Pool(dbConfig);

export const connectDB = async () => {
 let client;
 try {
  client = await pool.connect();
 } catch (error) {
  console.error('error while connecting to database', error);
  process.exit(1);
 }
 return client;
};

I have two queries as below

#1.

export const fetchUser = async (email) => {
const client = await connectDB();

  const query = `
    SELECT full_name FROM app.users
    WHERE  email = '${email}'
  `;

  let result;
  try {
    result = await client.query(query);
    if (result.rowCount) {
      return result.rows[0].full_name;
    }
  } catch (error) {
  } finally {
    await client.release();
  }
  return result;
};

#2

export const fetchWallet = async (email) => {
    const client = await connectDB();
    
      const query = `
        SELECT wallet_money FROM app.user_wallet
        WHERE  email = '${email}'
      `;
    
      let result;
      try {
        result = await client.query(query);
        if (result.rowCount) {
          return result.rows[0].wallet_money;
        }
      } catch (error) {
      } finally {
        await client.release();
      }
      return result;
    };

Now from one of my controller.js if I call these function separate await, no issues

ctrl.js

   const fullName = await fetchUser('[email protected]');
   const walletMoney = await fetchWallet('[email protected]');

No issues this way, however if I merge them into a single promise

   const $0= fetchUser('[email protected]');
   const $1= fetchWallet('[email protected]');
  
   const result = await Promise.all([$0, $1]);

this throws the below error

error while connecting to database Error: timeout exceeded when trying to connect at Error

Please suggest why this error is popping up & how can I get rid of it?

Thanks!