Also: check the cellar, basement, downstairs laundry. If there is a similar smell there, then it is definitely something wrong with the building.
My suggestion is to go and introduce yourself to your neighbours. Not too much, just a "Hi, my name is... we moved in last week, we're on the third floor". If you strike up a conversation, ask them to tell you if they know of any issued with mold in the building.
Yes! If you close everything up, including all the internal doors and cupboard doors, and go out for a few hours, when you come home your nose will direct you to the source of the smell. We once did exactly that exercise in a shared house, and managed to locate a potato that had fallen down behind the counter.
I know that putting a cut onion (slice large onion in half, no need to peel, place with cut side up) works for getting rid of fresh paint smells quickly, without the need for harsh chemicals. You could give it a go? Also, I've successfully burnt incense for a couple of hours to get rid of nasty mildew smells.
You might want to check the kitchen's plumbing and any damaged/old sealants.
Could be a tiny leak over a long period of time making the walls damp and causing the smell.
Also check the back of the dishwasher's drain hose, outflow pipe for any drips or problems.
I'll send you a bag full of the smell of my neighbours cooking. That will kill any smoke smells. That is if it does not kill you first
Australians obviously have immunity then
It’s likely going to be a challenge as there are areas behind cabinets and such which aren’t easily reached. Maybe take s closer look at that exposed concrete wall. Molds are found in many colors and can easily be overlooked. It can also be under paint or in cracks. Since a leak prone or area for water settlement is a good place to start, rule out the sink, floor, and under cabinet area. Do you have a dishwasher?
On pourous surfaces, the effect of bleach is often minimized as the mold may be inaccessible.
I would probably first vacuum as best as possible with HEPA level filtration. Then pass a torch over the bare concrete surfaces. Even if it’s not visible to the eye, the mold will burn.
For the musty smell, a dry powdered fungicide lightly dusted in the under sink areas can be very effective. I don’t know what the avalibility is in Switzerland, but something like Pirox should work.
A dust mask or respirator would be good if you seem to have a sensitivity to the environment.