Train tours?

There are some downsides to using traIns for guided tours. You would need to get a group from train stations to hotels. Meals between locations would be challenging. I'm sure there are more.

I was leary of bus time before taking my first RS tour, but I've found it's not a downside at all. The bus is only half full, so you can spread out comfortably, and there are stops every 1.5 to 2 hours. The guide uses part of the bus time to impart information about the next stop, or the area in general.

Since most trains in Europe are public transportation functions, it's less likely you'll
find a tour that uses trains. It also invites the question of getting between train
station and accommodation if there is a group of people - more chance of losing
people, pickpockets, etc, than if everyone is on the same bus going right to/from
the hotel and to/from sightseeing.

But, you can use trains to go between cities and then arrange day tours on your
own, if you're willing to do the work.

I found a company called Great Rail Journeys:
https://www.greatrail.com/us/destinations/europe/

There are some luxury rail tours, including this one in Scotland:
https://www.seat61.com/royal-scotsman-cruise-train.htm

There are some non-luxury ones in Ireland, as well. They uses buses to travel from the train stations, of course.
https://railtoursireland.com

There are RS tours that use trains for some portions of the itinerary. The Best of Spain Tour takes the train from Barcelona to Madrid. The Best of England tour takes the train from York to London. Family Europe tour takes the Eurostar from London to Paris. Several other smaller train trips are included in some tours, such as getting to Cinque Terre on some of the Italy tours when they stay in towns outside the 5, and in Switzerland. Other tours also use boats/ferries.

If you're concerned about bus time, know that the time on the bus is not all at once and will be broken up at least every two hours for rest stops (required for the drivers) or visits to interesting spots along the way. I have done five RS tours and only one day did I feel like the bus time was way too long, and that was due to an unexpected extra hour detour due to construction.

If you don’t like a lot of bus time, consider the RS Prague/Budapest tour. It only has one day on a bus and two great cities!

Great Rail Journeys is a well established company, I almost got a summer job with them in 2000 (until it turned out I'd got a real job offer....). A friend did one of their tours 2 years ago and had a great time, he was especially pleased with the local knowledge of the tour guide. BUT all of their european rail tours begin at London, usually around 09:00, and end there usually late afternoon. So from USA you would need two stays in London, although I suppose you could bail out at Paris or Brussels on the return journey, you'd only lose the final 3 hours. They use scheduled trains, the exclusive tours with private trains are much more expensive and often become more about the train than the places it calls at. .

The Brittanic Explorer is the most recent high end train in the UK. If you can afford it they have some interesting itineraries, with good looking days out.

In Scotland there is the Royal Scotsman, very luxury and swish.

For worldwide touring by train I've used Ffestiniog Travel from Wales. Very curated, small group tours. But they will also put together a bespoke tour, and have a considerable catalogue of hotels round the world which they have used on their tours. Almost all are individual, not chain hotels. Kind of a, possibly, better version of what RS does for hotels on his tours.
Carefully chosen for, in general, proximity to stations, without sacrificing quality.