NestJS: e2e testing using an axios-based client is not working as expected

I have a NestJS application that exposes some endpoints, and I have written a client application that I plan on releasing as an NPM package to work with the nest server. I am attempting to write end-to-end tests that start the nest server, connect it to a test database in a local docker container, and test it using the client. Here are some snippets of what I'm attempting to do:

Controller:

@Controller('/api/v1/messages')
export class MessagesController {

    constructor(
        private messagesService: MessagesService
    ) {}

    @Get()
    @UsePipes(new ValidationPipe({ whitelist: true, forbidNonWhitelisted: true }))
    private findAll(
        @Query() searchCriteria: MessageSearchDto
    ): Promise<MessageDto[]> {
        if (Object.keys(searchCriteria).length > 0) 
            return this.messagesService.search(searchCriteria);
        return this.messagesService.findAll();
    }
}

Client:

const http = require('axios');
const dotenv = require('dotenv');

dotenv.config();

export class MessageClient {

    public baseUri: string = process.env.MessageClientTarget ?? './';

    constructor() {}

    public async findAll() {
        return await http.get(this.baseTarget());
    }

    private baseTarget() {
        return `${this.baseUri}/api/v1/messages`;
    }
}

e2e Test:

describe('MessageController (e2e)', () => {
    let app: INestApplication;
    let client: MessageClient = new MessageClient();

    beforeAll(async () => {
        let moduleFixture: TestingModule = await Test.createTestingModule({
        imports: [AppModule, MessagesModule],
        }).compile();

        app = moduleFixture.createNestApplication();
        await app.init();
    });

    afterAll(async () => {
        await app.close();
    });

    it('/ (GET)', async done => {
        const { data: messages } = await client.findAll()
        expect(messages).toEqual([]);    
        done();
    });
});

And .env:

MessageClientTarget=http://localhost:3000

When I attempt to run this, I get the following error: "connect ECONNREFUSED 127.0.0.1:3000"

From what I understand, this is because the createNestApplication method doesn't actually start a server but instead creates a mocked version of the application.

My question is how can I work with INestApplication or TestingModule in order to start the application or what other way do I have to programmatically start a NestJS application. It is important to me that I perform the e2e testing with the Axios based client rather than supertest as a way of testing both the client and the server.

I have verified that the server is supposed to start on port 3000 locally, and I have verified that the client has the correct baseUri set. The address used by the client during testing is: http://localhost:3000/api/v1/messages and was verified by outputting the value to the console during the test. Also, only the database currently lives in a docker container and I have that running correctly. The whole application works perfectly when ran locally and it is only in the test that it is failing.