Just takes a moment to double check. Is the speedometer climbing if you give the engine a little fuel while in gear? While having the rear tires on the ground. If it is the transmission is probably okay.

It is a very remote possiblity for a cv joint to have brought the farm. Yet under no load conditions the rear wheels could turn like up on your jackstands with one bad.

The only reason I mention this to me it seemed strange you heard a rear tire chirp when entering third gear.

First to second is about the only point these five cylinder powerhouses might pull this off I supect. Second to third seems a real stretch. Now if you had a 240d automatic I would not question it.

This really is a long shot keep in mind. Just something I might check as it only takes a minute .