Mini Paceman Exhaust Treatment Malfunction

Engine light plus rough running and exhaust smell definitely points to an issue in the exhaust system. Since it's a gasoline engine, you won't have DEF fluid or associated problems. Have you checked the lambda sensor? A bad oxygen sensor can throw off the whole system, like a bad note can ruin a song. Is the catalytic converter heating up normally?

Lambda sensor, got it. Is there a quick way to test the oxygen sensor myself, or is it best left to a shop with proper diagnostics tools? I don't want to mess with the catalytic converter unnecessarily.

While there are ways to test it at home, you might cause more harm than good. It is possible to measure their signal, but in my experience, the engine light coming on is a pretty good indication they are toast. NOx sensors could also cause similar problems, but are less likely. If it was me, given the symptoms, I'd suspect the oxygen sensor and get it checked. After that, you eliminate the catalytic converter as the source of the problem and can breathe easily (no pun intended).

It was, indeed, the oxygen sensor. Got it replaced for 375€. Runs smoothly now. Thanks for the insight!