$factory could be documented as * @param string|callable $factory, right?

Could you add a short example and/or a link to some article explaining how using factory helps with testing?

Correct. Docblock could be updated for $factory parameter. I didn't do that because other methods don't have params described either.
I can add test to https://github.com/Naktibalda/codeception-laminas-tests similar to https://github.com/Naktibalda/codeception-laminas-tests/blob/master/tests/functional/AddServiceToContainerCept.php.
General principle behind it is that whenever you use ServiceManager#build() to build a service, new service instance is returned. In order to have expected service stub built by the ServiceManager we can return it with help of substitution of factory for the service in tests.

I didn't do that because other methods don't have params described either.

That's because @TavoNiievez went through all methods and replaced @param annotations with scalar typehints.
$factory can't have typehint, so @param provides useful information for IDEs and static analysis tools.

General principle behind it is that whenever you use ServiceManager#build() to build a service, new service instance is returned. In order to have expected service stub built by the ServiceManager we can return it with help of substitution of factory for the service in tests.

I'm not asking for myself, but for people who may want to use it. I tried searching yesterday, but failed to find anything relevant.

Example:

$I = new FunctionalTester($scenario);

$foo = \Codeception\Stub::makeEmpty(stdClass::class, ['bar' => 1]);
$I->addFactoryToContainer('foo', fn() => $foo);

$I->amOnPage('/edit');
// EditController
//public function editAction()
//{
//    // $service is a Stub created earlier
//    $service = $this->serviceLocator()->build('foo', ['param1' => 'test']);
//}

More info about shared/non-shared services:
https://docs.laminas.dev/laminas-servicemanager/configuring-the-service-manager/#shared