With the 2018+ Macs, many of the parts are paired to the Logic Board now. Which parts are paired vary between models. Even something as simple as a Lid Angle Sensor is now paired to the Logic Board, so swapping a simple Lid Angle Sensor between to laptops won't work. Even an Apple or an AASP will be unable to make it work since the Apple service utility cannot pair some components a second time...the Lid Angle Sensor is one of them...yes you must pay to replace a working Lid Angle Sensor when the Display Assembly is replaced because Apple's service configuration utility cannot re-pair (aka pair again) the original sensor, TouchID is another. My organization has had to pay to replace good working parts because of this....it is not right at all.
Probably what the tech meant was an Apple service configuration utility must be run to pair the new components, but as I have already mentioned this is not possible. That utility will only pair new parts since it requires Apple having the correct part serials numbers on file to ensure the proper part is being paired.
Unfortunately these days, third party repairs are becoming a thing of the past for Apple products. Many times you will end up losing some functionality of the device. Even techs that may perform board level repairs by soldering replacement chips & components onto the board....even this is becoming more difficult since many of the chips needed are not available or cannot be swapped due to the security changes & pairing issues.
And as someone else mentioned, it is possible the tech damaged something or the replacement part had a bad camera or cable. Your beef is with the repair shop not properly advising you on possible consequences of an unofficial repair, or due to their own negligence in damaging the laptop/part, or installing a part that was not fully functional.
Apple is not friendly to the Right to Repair movement although they may make some rudimentary gestures. Some other OEMs are a bit better for allowing third parties to repair their products.
You can always leave Apple product feedback (Apple won't respond) or you can contact Apple corporate to voice your displeasure at the lockout of third party repair centers. Don't expect Apple to care since their focus is elsewhere.