Smart casual. There are dress restrictions for breakfast I think its no tracksuits or trainers. But I'd check with hotel.
At the restaurant Enoteca the whole family was dressed smart casual. No problem.
As far as I can recall, smart casual dress code for dinner will be OK
I am guessing- but no suit. A sports jacket would be appropriate even though you'll probably see everything there.
Get an answer from Kempinski Grand Hotel des Bains St. Moritz staff and past guests.