I think there's 2 separate things at play.

Most products don't require testing by a notified body. That means anyone can do the testing - or even you could do it at home. The CE mark is self-assessed - you don't have to get a lab to issue it to you.

But electronics does have to conform with various electromagnetic compatibility rules. There's effectively no way to prove that without doing EMC testing. Most non-EU manufacturers will still do EMC testing in a lab, perhaps in China. That test report becomes part of the product's technical file.

My point is that if you take a module from a 3rd party and integrate it into a larger electronic product, it no longer has the same behaviour from an EMC point of view. You have no evidence that it meets the harmonised standards for electromagnetic compatibility. Realistically, probably nobody will ever notice. But if they do, you don't have evidence that your product complies with the standard.