I lived there for awhile in Lausanne. I think three weeks to a month is a good amount of time to really get a feel for the place, meet some locals, and slow down a bit.
The trains are efficient, clean, and easy to use.
I highly recommend staying on or near Lac Léman in one of the small lakeside towns for a week and exploring the countryside from Lausanne to Montreaux and beyond. The Swiss wines are excellent and you won’t find them outside Switzerland because the Swiss drink all the wine they produce!
Of course I know you will take the train from St. Moritz to Zermatt.
While In Zermatt spent a few days to hike around. Take in a mountain restaurant - Riffelhous is a good one.
There is a really interesting cheese experience in Gruyere. I’m sure there are others in different towns. You sample the grass the cows eat, taste the cow’s milk, and then taste the cheese made from it.
The Swiss Post busses will take you anywhere mail is delivered and for a reasonable price. This is an experience in and of itself.
The Swiss Alpine Club runs a series of high mountain huts. It is very easy to plan a hut to hut hiking trip and carry just a small daypack with you.
https://www.sac-cas.ch/en/
All the major cities are worth exploring - they are easy to navigate, clean, and safe. Most have an historic central city area and markets.
One thing I would caution about - there are only so many castles, museums, and cathedrals you can visit before they all start to look the same. So choose a few really interesting ones and skip the rest.
To me the magic happens on the byways and in the small towns.
Tom