You can introduce a delay by using promises. Where we use setTimeout inside the promise to resolve after a certain period.

function delay(ms) {
  return new Promise(resolve => setTimeout(resolve, ms));
}

Usage will be like below:

it('test timeout', async () => {
    service.getData('2025-10-12', '2025-10-16').subscribe(
        {
            next: data => {
                expect(data).not.toBeNull();
            },
            error: error => {
                expect(error).toBeNull(); // handling all missing keys
            }
        }
    );
    // mocking endpoint - binding
    const response = httpController.expectOne({
        method: 'GET',
        url: RestServerSA.RELEASES_OVERVIEW_RANGE
    });
    await delay(5000); // delay for 5 seconds
    // or
    // await new Promise(resolve => setTimeout(resolve, 5000));
    // mocking response from endpoint
    response.flush({});
});

You can also try a combination of fakeAsync and tick, but I do not favor this, since it already similar to flush.

it('test timeout', fakeAsync(() => {
    service.getData('2025-10-12', '2025-10-16').subscribe(
        {
            next: data => {
                expect(data).not.toBeNull();
            },
            error: error => {
                expect(error).toBeNull(); // handling all missing keys
            }
        }
    );
    // mocking endpoint - binding
    const response = httpController.expectOne({
        method: 'GET',
        url: RestServerSA.RELEASES_OVERVIEW_RANGE
    });
    tick(5000); // delay for 5 seconds
    // mocking response from endpoint
    response.flush({});
}));