Best time for RST to Switzerland

It is good to go mid May (I will be there for the 5th two weeks from today) through September.
If you are doing it yourself the best time to go up to any mountain is as early as possible for the best visibility and to avoid crowds.

I would certainly do September--I went in October 2022 independently and it happened to be the warmest October on record. I was pleased with the weather and crowd size.

September is good but exact timing depends on where. We have found Pontresina, for example, gets pretty darn chilly later in the month whereas we enjoy the Lauterbrunnen Valley into October and have been there as late as the 19th. In the west, the weather along Lac Leman (Geneva) is lovely well into the fall in our experience.

Train stations and some lifts are busy all the time (Lauterbrunnen Bahnhof has massive tour groups some days) but once out on a trail, it thins out, generally, although the most congested hike we’ve ever taken was in September in Pontresina last year.

Spring is too early, as many of the lifts aren't open yet.
I've been in Switzerland twice in Sept and Oct. , and it was great. The cities may be in the 80's, which caught me offguard, but the mountains were delightfully chilly. Double check when things start closing in late Oct., (such as lifts for maintenance. )Have a fantastic trip, I'm jealous, and ready to return!

I recommend late August-late September. The crowds leave around the 3rd week in August but it’s still nice out. If you go in May a lot isn’t open in the mountains. Mid/Late June is also okay.

I LOVE Sept/Oct for the added bonus of so many cultural festivals, ie: Weinfeste, Bierfeste, Alpabfahrt (cows coming home from high pasture). 11 of my 12 trips, I had beautiful weather!