In the EU (and UK with UKCA), CE certification is down to whoever makes the product available on the market. There's no get out for pre-certified modules. If you put a pre-certified module in a box and sell it, you have to be responsible for the CE mark.

You need evidence that the whole product complies with the EMC regulations. There's some judgement involved - if you put a certified circuit board in a plastic box, it won't change the EMC behaviour so you don't need to re-test. But if you solder a module onto a larger circuit board, you are almost certainly changing the EMC behaviour. You should definitely be re-testing something like that.

The pre-certified module does save you some time in the "intentional radiator" testing - assuming you use the same antenna it was tested with as a module, you can probably make the case that the behaviour is the same.

Will anyone ever notice or care for a few thousand niche devices? I doubt it. But to sell in the EU legally you do need to do that testing.