The places you mention, particularly the Jungfrau region (known best as the Berner Oberland), Lugano, and Como, are all going to be busy with tourists in summer. That is the reality of travel at that time. The best strategy is to book your lodging early, and focus on the mountain villages rather than cities like Interlaken or Bern.
Last September we took our son’s family, with twin boys age 11, to Switzerland and Italy for a hiking vacation. The September dates meant taking the boys out of school, but that was our daughter’s request, to avoid summer heat and crowds. It was nice and quiet in Mürren, where we shared an apartment, and in the Dolomites (Alpe di Siusi). But the trains were packed, especially in Italy. We experienced the same crowded trains this year in late September and early October, especially in Italy. In Switzerland I booked us into first class for a less crowded experience.
In spite of the crowded trains, I would not recommend renting a car, as you don’t want one in the car-free villages of the Berner Oberland, and taking a rental car from Switzerland into Italy to turn it in there will incur a huge drop fee.
Pat has given you a nice itinerary, but since you are interested in hiking and avoiding major crowds, I suggest you skip Luzern and add more time to Pontresina. Luzern is a busy city crowded with tourists, while Pontresina is a mountain village that is a bit off the main tourist path, at least compared to the Berner Oberland and Luzern. The area of the Engadine offers beautiful hikes, including in the Swiss National Park.
https://www.pontresina.ch/en/guide/aktivitaeten/hiking
https://nationalpark.ch/en/
The Bernina Express will take you to Tirano in Italy, and you can change trains there to one heading to Milan via Varenna on Lake Como. This is a lovely town but it is very popular and you may have trouble finding lodging in mid-summer. We have not found any nice long hikes there, but they may exist. We have hiked up to the old castle, but the trail is shared with mountain bikers, which makes it less than ideal.
http://www.castellodivezio.it/EN/home-en.html
You asked about favorite experiences. Ours, from a number of hiking trips in Switzerland (including the 2 most recent, in 2023 and 2024), is hiking in view of the Aletsch Glacier at Bettmeralp. Scroll down on this web page to see some photos:
https://www.aletscharena.ch/en/aletsch-arena/places/bettmeralp
In reviewing what I just wrote about packed trains in Italy and crowds at Lake Como, I am debating whether I should advise you to skip Italy and stay in Switzerland. Our recent trip included 2 weeks of hiking in Italy, around Lago Maggiore and Lago di Garda. None of it was anywhere near as beautiful as the hiking we do in Switzerland. At Lago Maggiore, where we spend a full week, it was hiking on mule tracks in nice forests, with no views. One day at Lago di Garda, hiking on Monte Baldo, could have been very scenic, but the views down to the lake were totally obscured by fog.
But if it is amazing food you are after, I will say that is easier to find in Italy. I still chuckle when I recall our grandsons’ (the twins) reaction to our first dinner in Italy, in the patio at our hotel in Desenzano del Garda, on the lake. We had a long difficult travel day, and did not arrive at the hotel until 8 pm, but they were expecting us with a nice table ready for 8. These kids are serious and discriminating eaters (I guess the current term is “foodies”) and they especially love all kinds of fish and curious crustaceans. When the food started coming, beginning with antipasti and on to primi and secondi, they were as happy as the proverbial clams. The staff was enchanted with their reaction, and started bring little bits for them to try. . . . And then there was breakfast, with pastries.
After that experience, and the Dolomites and then Venice, they didn’t want to leave Italy.