Try below code and make sure the function contains await keyword should always async function (async keyword should be used before function name). But in your case callback function already defined as async function.

Just change the saving part alone to below, you are good to go.

try {
    const catModel = mongoose.model('testColl', catSchema);
    const cat = new catModel({ name: 'Zildjian' });
    const response = await cat.save(); // if error while saving, catch will get executed
    console.log(response); // saved record
    // return success response 
} catch (err) {
    console.log('err' + err);
    // return error response
}

First you need to make connectDB async and then git rid of mongoose.connection.once() as you otherwise would need all your Mongoose code to be in there.

main().catch((err) => console.log(err));

async function main() {
  await connectDb('testDB');

  const catSchema = new mongoose.Schema({ name: String });
  const catDocument = mongoose.model('testColl', catSchema);

  const catObj = new catDocument({ name: 'Zildjian' });
  await catObj.save();
}

connectDB

import mongoose from 'mongoose';
import { strict as assert } from 'assert';
import { readToml } from './readToml';

const db = readToml('./config/database.toml');

export async function connectDb(
  database: string = db.database,
  uri: string = db.uri,
  username: string = db.username,
  password: string = db.password,
) {
  assert(typeof uri === 'string');
  assert(typeof database === 'string');
  assert(typeof username === 'string');
  assert(typeof password === 'string');

  const URI = `mongodb+srv://${username}:${password}@${uri}/${database}?retryWrites=true&w=majority`;

  const options = {
    bufferCommands: false,
    autoCreate: false,
  };

  try {
    await mongoose.connect(URI, options);
  } catch (err: any) {
    throw err.message;
  }
}

In order to use await you have to provide a promise to await for. cat.save() returns a promise, so this should work. Nevertheless you can also only use await in async function, so you should also declare the callback function for the open event as async:

(async () => {
  connectDb('testDB');

  mongoose.connection.once('open', async () => {
    console.log('MongoDB is connected');

    mongoose.connection.db.listCollections().toArray(function (err, names) {
      console.log(names);
    });

    const catModel = mongoose.model('testColl', catSchema);

    const cat = new catModel({ name: 'Zildjian' });
    await cat.save();
    console.log('Saved in db');
  });
})();