is there any way to Connect oracledb using typescript ES6 class and module?

The actual reason for your error

TypeError: this.conn.execute is not a function

Is because the this.conn is most likely undefined. Add a check like this.

public getRwCnt() {
  if(this.conn === undefined){
    console.log("The connection is not ready yet.");
    return;
... // Rest of your function
}

But this will only highlight that you have a problem, but not tell you why.

The reason is that your constructor is strictly synchronous. Consider having a function that waits for the constructor to finish.

Here is a version that works:

import * as OracleDB from 'oracledb';

export class ConnectionDAO {
  /**
   * Connection Variable Declaration
   */
  public conn: OracleDB.IConnection;
  public connProm: OracleDB.IPromise<void>;

  /**
   * Result Variable Declaration
   */
  result;

  /**
   *
   * Creates an instance of CommercialDAO.
   * To Initiate Connection and Make the connection utilized by @memberof CommercialDAO
   * @memberof CommercialDAO
   */
  constructor() {
    this.connProm = OracleDB.getConnection({
      user: "hr",
      password: "hr",
      connectString: "localhost/XEPDB1"
    }).then(async (connection: OracleDB.IConnection) => {
      console.log("Connection finally created in constructor")
      this.conn = connection;
    }).catch((err: any) => {
      console.error(err.message);
    });
    console.log(" - Dumping Connection state in the end of the constructor", {conn: this.conn} , {connProm: this.connProm} );
  }

  public getRwCnt() {
    let me = this;
    return new Promise(async function (resolve, reject) {
      try {
        console.log(" - Dumping Connection state BEFORE waiting",{conn: me.conn} , {connProm: me.connProm} );
        await me.connProm;
        console.log(" - Dumping Connection state AFTER waiting",{connServerVersion: me.conn.oracleServerVersion } , {connProm: me.connProm} );
        let result = await me.conn.execute('SELECT count(*) FROM employees');
        resolve(result.rows);
      } catch (err) { // catches errors in getConnection and the query
        console.log("[Error] happened? - calling reject",err);
        reject(err);
      }
      if(me.conn) // Only release it it if it actually is set
        me.conn.release();
    });
  }
}

const d = new ConnectionDAO();

d.getRwCnt()
  .then((result)=>{console.log("RowCount",result)})
  .catch((err)=>{console.error("Promise rejected - ",err)})

console.log("Object constructor returned");

Running this with ts-node gives this result

 - Dumping Connection state in the end of the constructor { conn: undefined } { connProm: Promise { <pending> } }
 - Dumping Connection state BEFORE waiting { conn: undefined } { connProm: Promise { <pending> } }
Object constructor returned
Connection finally created in constructor
 - Dumping Connection state AFTER waiting { connServerVersion: 1804000000 } { connProm: Promise { undefined } }
RowCount [ [ 107 ] ]

Seems you use the this with wrong way in function getRwCnt().

Remember each function in JavaScript has self this.

Option 1 Assign the top this to another variable at the beginning of function

public getRwCnt() {
    let me = this; 
    return new Promise(async function(resolve, reject) {
        try {
            let result = me.conn.execute('SELECT TESTCASEID FROM EXECUTE_TESTCASE');
            resolve(this.result.rows.length);
        } catch (err) { // catches errors in getConnection and the query
          reject(err);
        } 
        me.conn.release();
      });

Option 2 Use ES6 Arrow function

public getRwCnt() {

        return new Promise(async (resolve, reject) => {
            try {
                let result = this.conn.execute('SELECT TESTCASEID FROM EXECUTE_TESTCASE');
                resolve(this.result.rows.length);
            } catch (err) { // catches errors in getConnection and the query
              reject(err);
            } 
            this.conn.release();
          });

I tried your solution, but looks like typescript is not waiting for the call await me.connectionPromise; Also, not sure if the connection is successful or not. I am getting below output.

Inside constructor
get Connection executed....
 - Dumping Connection state in the end of the constructor { conn: undefined } { connProm: Promise { <pending> } }
Inside getRowNumbers function call....
Connection state BEFORE waiting:  { conn: undefined } { connectionPromise: Promise { <pending> } }
Object constructor returned

Somehow below output lines in your code are missing for me.

Connection finally created in constructor
 - Dumping Connection state AFTER waiting { connServerVersion: 1804000000 } { connProm: Promise { undefined } }
RowCount [ [ 107 ] ]

I had same issue. Replaced my import:

import * as oracledb from 'oracledb';

with

import oracledb from 'oracledb';

Fixed it for me