Avantime lambda sensor issue

Sounds like it could be. Exhaust leak and smell points towards something like that. Have you checked the catalytic converter for damage? Could also be the EGR valve. Is the smell stronger than usual?

I've visually inspected the catalytic converter and it appears intact. I'm not familiar with the EGR valve. Is there any way to test the lambda sensor to confirm it is defective?

Testing a lambda sensor requires specific tools. Given the exhaust leak and the smell, it's hard to say for sure without proper diagnostics. I suggest taking it to a workshop.

I took the vehicle to a workshop, and the lambda sensor was defective. The total repair cost, including parts and labor, came to 375€. The car runs perfectly now.