I see that a PCB requires certification even if it incorporates a certified RF module, so EMC tests for spurious emissions will still be needed. Is FCC-approval needed if a Raspberry Pi is shipped/sold with a USB WiFi dongle? So how is modular integration actually defined? Are EMC tests for spurious emissions needed when a USB WiFi dongle is connected to a Raspberry Pi? Or is it that FCC doesn't consider integration via USB isn't considered to be "
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.
The Raspberry Pi has it's own FCC ID: https://fccid.io/2ABCB-RPI32
Presumably the RF module does also.
You should check that the FCC IDs for both pieces of hardware are actually valid, and were tested using the devices that you intend to ship, as there are very many manufacturers that will "blindly" stamp whatever FCC ID on a product in order to say it has a number, even though that number is for a different product and the certification doesn't apply. That seems to get it though border clearance currently, but if they ever tighten that you might be in a pickle with invalid IDs.
If both have FCC IDs then you can likely get away from having to do any testing and still have a commercially viable product. Without testing the entire device your Declaration of Conformity (DOC) is based on the testing of the devices individually, and they technically can't be shipped in the same box (however many many manufacturers do that and aren't penalized). The penalty that you are at risk of is having your shipments to USA held up while you prove that they conform, which rarely happens, but when it does it's probably not convenient, and government agency fees/fines could mount up! Seems like it would have to be willful, egregious and impactful before it would really pop on the FCC's radar though, considering the large volume of eBay product that enters the country (USA/Canada) on invalid IDs.
Having a full system EMC test allows you to quickly send a document that proves what you say on the DOC is true, and would allow you to send the device with the module installed, with your head held high, and no worries that your competition would try to rat you out and possibly make a big deal out of it.
You're not alone in navigation of the bewildering path of certification, though...
Specifically to your questions:
Is FCC-approval needed if a Raspberry Pi is shipped/sold with a USB WiFi dongle?
Technically yes, practically and following other successful manufacturers' examples, no. "No" carries more risk. The exact definition of "with" is the gray area.
So how is modular integration actually defined?
FCC recognizes modules as separate from the main system, so if you build a board from scratch, you would need to have an EMC test that shows that the board alone meets FCC- Class B (or A, whatever your target), and that the module has valid FCC certification. In this case you state on your documentation and box "Contains FCC: xxx-yyyyyy" (for the module), but you don't need an FCC ID for your device in most cases.
Are EMC tests for spurious emissions needed when a USB WiFi dongle is connected to a Raspberry Pi?
If shipped/purchased together then yes, otherwise no. Nobody seems to actually follow that, though.