Driving from Italy to Switzerland: any custom check?

You will indeed pass through a customs post, where you may, or may not, be asked to pull over for an inspection. If you have any goods to declare you must do so, if you have any invoices that need stamping to claim back tax idem.
But there will not normally be an immigration check, as Italy and Switzerland are both in the Schengen free travel area.

In 2017, I went across Bodensee by boat from Lindau to Rorschach, Switzerland, then traveled by train to Bregenz, Austria, and back to Lindau, Germany. I never saw any customs check, or, of course, immigration on the trip.

Reynard,

No matter where you enter from don't forget to get the Swiss Vignette to stick on your windshield. It's 40 swiss francs for 2023.

Or even better, don't drive! Then you won't have to worry about it.