MBP fan running but no airflow
How are you so sure that there is no air being moved around?

Further, when does the throttling apply - right at the start or after some time? Because at some point under high load, you will experience some throttling on basically any laptop.

The only thing - depends on how familiar you are with such things - I can think of, is taking the back cover off and literally looking at the parts. Yet, I would not necessarily recommend this.

Before doing something like this: Save your data either in a backup or by copying your files.

Apple might be able to help you, but what usually do and recommend is going to a certified repair shop. It's more personal and you usually speak directly to the repair guy. Though, I guess they will probably not be able to do anything different than what you did, @Tetsujin or I suggested.