Switzerland is genuinely a country of several distinct cultures sharing one federal structure — German-speaking in the north and centre, French-speaking in the west (Romandy), and Italian-speaking Ticino in the south, plus a small Romansh-speaking area in the east. Each region has its own dining rhythms and café culture.
German-speaking Switzerland tends toward efficient, no-fuss café terraces where a dog beside the table draws no particular attention. French-speaking Switzerland leans into a more leisurely, French-influenced café culture, with terrace seating similarly relaxed about dogs. Italian-speaking Ticino, closest to Italy both geographically and culturally, has an outdoor dining style that will feel immediately familiar if you've travelled with a pet in Italy.
None of this changes the practical rules — restaurant etiquette and leash law both stay whatever the specific venue or canton sets — but it's a genuinely enjoyable way to experience one small country feeling like three or four different ones over the course of a single trip.