This is certainly not the place to ask for legal or regulatory advice, but my quick 5 minutes on Google suggests that it is only future certifications to be performed by the new smaller set of labs. Existing certification is still verified (on an ongoing basis) by market purchases, so should not be subject to any lower standard today or in future. A fraudulent test report is still no defence for shipping non-compliant product.
Where there could be problems is for product intending to reach compliance before the cut-off, but failing to make the deadline for some reason. In that case you'd need to repeat the testing.
Assuming the rules are for honest reasons, I guess the change is because the number of different products is increasing, and market sampling is becoming less effective at catching incorrectly certified products.
You will need to pass FCC 47, section 15 to show that you conform to the EMC standard for the USA. The tests are required for your product, as it is an intentional emitter, as well in an unintentional emitter.
If you are looking at other markets, you'll see you have other standards which you'll have to meet. Pick up your mouse, keyboard, monitor, computer, and you'll see a plethora of other logos along with FCC: CE, CASA, CAS and others. There is a different set for different countries, or groups of countries, most are defined in this document here: https://www.ieee.li/pdf/essay/guide_to_global_emc_requirements_2007.pdf
In answer to the "how do other companies deal with this" is they do lots of testing and follow any read-across that they can find. Most test houses will be happy to help with this.
Don't forget, if the IoT device is to go in a car, it will need to conform to the automotive standards (which has even more variation than home equipment) and there are also medical and military standards which may have an influence depending on your device and where it ends up.
My advice is to contact a local test house and ask them what they recommend for your target market.
Best Answer
Assuming (1) that the USB dongle itself is approved as a computer peripheral and (2) the dongle has not been modified, then I believe the dongle is considered a separate and independent product (non-module) and does not need an additional approval to be sold with the Pi.
The safest best is to include the dongle in its original packaging and let the user plug it into the Pi. The of course means that you need to make the Pi's USB port user accessible.
If instead you want to include the dongle already plugged in and the assemblage is contained in a non-accessible enclosure, then I think you need to do verification testing on the resulting assembly and label the outside to indicate that the approved transmitter is located inside. This makes sense since a person inspecting the full device would otherwise have no way of knowing what certification that are relying on - or even that there was a certified device was inside.