Hi Sohaib,
I understand your confusion and actually tend to agree that in most cases if the wireless charging works but the wired port doesn't, the normal fix is to replace the charging port. On your phone it's relatively straight-forward; the charging port is on a ribbon cable all by itself so changing it doesn't affect anything else in the phone.
However, I guess it depends how much trust you have in the repair shop. I would assume the first thing they would have tried would be to replace the charging port, and it sounds like they most likely did that but found that it didn't fix the problem. Although ultimately the wireless charging signal and the power coming from the USB port both have to make their way through the charging IC in the phone to get to the battery, there are different electronics in play before they get there, so it is indeed possible for this to be a motherboard issue, specifically a capacitor in this case,.
You could try replacing the charging port for yourself; it's not too bad of a job, although that rear cover is really glued on well on those Samsung phones, but if it's been opened recently it might not be as difficult as normal. Here's the iFixit guide showing you how to do that job.
[guide|141976|Samsung Galaxy Note20 USB-C Port Replacement - iFixit Repair Guide|new_window=true]
Of course, you could also take it to a different shop and get a second opinion; different shops have different levels of expertise so not all shops can fix all the same problems. If they correctly identified a particular capacitor as the problem and have the equipment and expertise to replace it, it's not all that big of a job, but I assume they don't do board level repairs. You might consider finding a shop that does if a new charging port doesn't do the job.