Accessibility

Nearly all trains involve climbing and descending 1 -4 steps to board/alight. Often, not always, steps may be required to get to the proper train platform, though many larger train stations have elevators or escalators.

IF train changes are involved on a journey, there may be a bit of a crowd rush to board.
Seats can be reserved in advance; it is then up to the passenger to find his car and seat while traversing the aisle.
First class train seats tend to be less crowded, and often slightly larger.
Train tickets can be bought in advance on the swiss app, schedules with tracks can be perused in advance too, so that you are well positioned.
Doable, but may require a little more research.
Many train trips are quite scenic, and a picnic lunch can be brought aboard.
As for cable cars up, I think if the staff were made aware of your need in advance, they may be able to offer some help.

I found that most of the trains I rode in January in Switzerland had entrances at platform level. The only one I had to climb up was an IR train from Luzern to Zurich.

The Rigibahn is fairly easy. Go 2nd class so you do not have to walk up the stairs to the 1st class deck on the boat ride to Vitznau.

I will let our Swiss travel experts talk about trains/lifts/gondolas, and the challenges of cars outside the cities. When looking at hotels, search for those with elevators and minimal stairs at the entrance. Booking.com is frequently recommended for searching because of the filters you can use to refine your choices. But my main comment is in reference to your use of a transport chair. Given the high likelihood of cobblestones and uneven pavement, and curbs without cutouts, a transport chair is not a good choice. The small wheels make for a rough ride, and often can't negotiate uneven surfaces. Plus, the seat is not meant to be sat in for any length of time. Its really meant to get from one place to another in a short distance and a few minutes. A folding wheelchair of the correct size will be both more comfortable, and easier to manage with its large rear wheels.

The Sage Travelling website may be of some help, since they specialize in accessible travel.

So here in Switzerland we have a new law on accessibility and it requires ALL public transport to be "low roller", that is the good news, the bad news is that the projects should have been finished by the end of June, but they are running a little late. But by next year, you should be good to go.

I'm Irish by birth, Swiss by choice and have some mobility issues. I'd say our public transport systems here in Switzerland are very supportive and I have always found them to be very helpful. Have a look here: Travel with reduced mobility.

Generally speaking you need to keep in mind that Europe is much older, the houses and streets are small are and as many of the buildings are of historic interest there is little opportunity for introducing accessibility features. So you'd be well advised to contact the accommodation you are intending to use and ask about what they can do. I have found most places have a few ground floor rooms or a kitchen service elevator they will let you use if you ask them. Or if they can't provide service for you, they usually can suggest some where to stay instead.

I too can't stay standing for long so I carry one of those Helinox light chairs. They are fairly light and back down well to find in a day sac.

Hope it all works out for you and enjoy your trip.

As Jim mentioned, there have been many recent improvements that enhance accessibility. Train platforms have been raised, and the same applies to bus stops, making it easier to board without needing to step up. Additionally, ramps have been installed at train stations that previously didn't have any, and elevators are occasionally available.

However, German trains, which typically operate on the Zurich to Interlaken route, are not as easy to get into. In cases of service disruptions, older train cars with steps may be used, so the system isn’t perfect yet. It's advisable to ask for information at the train station to find the best routes for your needs.

If you plan to stay on a mountaintop, I recommend opting for mid-June rather than early May. While snow is still possible in both periods, there’s a greater chance of clear ground in mid-June.

Please note that the Einstein House is a small apartment on the second and third floors of an old building, and it's unlikely to have an elevator. I have been there before but took the stairs, so I am unsure. The Einstein Museum, housed in the Natural History Museum in Bern, is far more interesting and provides accessibility information on this page:

https://www.bhm.ch/en/visit/practical-information

As you continue to plan and narrow down your itinerary, feel free to post here for feedback. For instance, those who have visited Gruyère can inform you that it consists mostly of cobblestone streets and involves a lot of uphill walking.