Sometimes on the housing market there are houses called "chalet" which look and smell more like a house with all its amenities than a wooden hut.

May such a building be used as a legal primary residence, i.e. inhabited year-round, with address and corresponding registration at the local commune?

I don't think, there is a problem with that.
After all, what the various communities really hate is all the cold, empty chalets that are only inhabited twice a year for a fortnight....

That's why, e.g. in Graubünden, you can only buy a chalet if you rent it out for most of the time you are not using it (at least, that's how I understood it).

If you live there, you pay taxes there.
If you use the local shops and have the renovation done buy a local contractor, you'll soon be on a first-name basis with everyone ;-)

It depends on the designation of the building is a holiday home or not, the designation can usually be changed, you should enquire.

You can try, but if you do not live there there is a good chance that the mailman will shop you... (someone very close to me had this happen to them and they almost ended up losing their permit as a result....).

There are 'chalets' and then 'chalets'. Some are owned by millionaires and some are just nothing more than 'huts'. Just depends. Many lake side chalets are threatened by demolition because they were never supposed to be lived in, like on the south side of Lake Neuchatel, in nature reserve areas. People bought them as holiday chalets and slowly enlarged them and added more and more amenities, against local rules.

Just out of interest how is the primary residence decided?

If you stayed 4 night per week in one place and 3 in another would the deciding factor be the time or are there other factors?

If I understand correctly, can one designate a chalet as a primary residence, then yes, it can be done. But there is often quite a grey area, in determining primary vs. secondary residences. Do not think, that if you buy a chalet, visit 2x a year, and then live, work, children go to school in/around your secondary residence. This indeed will be 'found out' by those concerned.

Generally if you spend more time in place A vs. B, and have closer ties to A vs. B, then A will be your primary residence. However, I know of some very delicate sitations that often have been discussed with the two communes concerned to come up with a solution.

My question wasn't focused how to pretend that a given chalet is one's primary residence, but whether a chalet build out of regular residential zone can also serve house-like purposes. I.e. there is the zoning to protect the land against urban-sprawl, so I thought having a full-fledged residence there would be in violation of these laws.

Only your Commune/Gemeinde can tell you.

If there is a chalet that is a livable structure and zoned as residential with say 25 m3 of living space, then one can live there. But one cannot change the space to say 50 m3 of livng space without going through the proper procedures, and one cannot say start a business or industry in such chalet, as it is residential.

Alternatively, if you are talking more about these garden huts that are often leased garden spaces to have a garden, then no they are not zoned as residential living space.