It turns out the previous owner had two cats and they have made one or more "deposits" in one of the bedrooms and perhaps at other locations. Apparently, the smell was "woken up" when we professionally cleaned carpets.
The smelly area is not stained at the carpet level so the previous owner most likely attempted to clean the mess, at least partially. Unfortunately, improperly cleaning cat urine makes further cleaning harder and I do not know what was done so I can only test cleaning techniques and hope they’ll work.
I started by dropping a whole bottle of Nature’s Miracle directly on the carpet, soaking the affected area. I did wait for it to dry completely but the smell persisted (you must wait for it to dry completely because it contains enzymes which break down the smelly agent).
Yesterday, I removed the carpet and padding. I planned on replacing the carpet anyway. This revealed that while not stained, the underlayment smells so it was most likely in contact with the urine for some time. It smells but much less than the carpet / padding though! I took the carpet / padding far away from any nose. The smell is not as strong as it used to be. Ah, some progress made.
I am going to use more Nature’s Miracle directly on the wood. I hope I will not have to replace the underlayment. If the treatment is sucessfull, I will use Zinsser B-I-N Primer / Sealer to further block odors, just to be sure. Improperly cleaned cat urine often resumes smelling on humid / warm days and I want to avoid this!
Here is the underlayment board in question. Two stains are clearly visible: