Passat Tiptronic: Faulty Reverse Gear

'Hello, I own a Passat TDI PD 1.9 l, first registered in July 2000, with 160,000 km on the clock. After I recently replaced the engine due to a tire blowout, the car ran perfectly for 8 weeks. However, this weekend, the Passat stopped reversing. While it's possible to engage reverse gear ('R'), unfortunately, nothing happens. The gear selector is displayed correctly on the instrument cluster, and the reverse light works, so I suspect the problem isn't with the gear linkage. When I checked the error memory, there were no error codes. The local VAG dealer told me that a new transmission needs to be installed (approximately 3,500 EUR). This is a significant amount of money that I'm not necessarily willing to spend. Perhaps someone in this forum can help me with troubleshooting or has some tips on this issue.'
Best regards, Olaf.