avoiding stairs at tube and train stations in London

Most larger stations have both escalators and lifts and are pretty accessible.

All of your journeys stated above will use St. Pancras/Kings Cross, the stations are connected.

To go other places, use the official journey planner: https://tfl.gov.uk/plan-a-journey/?cid=plan-a-journey

Once you enter your start and end point, you can go to "Preferences" and set for different accessibility options

The good news is the train to York and the train from Edinburgh both operate from Kings Cross. It's step free.

The Eurostar is at St. Pancras which is across the street from Kings Cross. Also step free.

However, you will have a step or two getting on and off the trains.

Here's information on which stations have step free access with local transport.

https://stepfreelondon.uk/map/

This is the home page to the accessibility part of the TfL website- this has a huge amount of resource on it- https://tfl.gov.uk/transport-accessibility/

Note the travel assist service, which you can use- either by pre-booking or as a turn up and go service, also the section specifically about planning an accessible journey.

Where are you staying in London? There are a number of tube stations that are very stairs heavy and you will want to avoid them. It would be better if wherever you stay is close to a fully accessible tube - that will make things a lot easier for you.
If you haven't fixed up accommodation yet then looking in the immediate area around King's Cross/St Pancras would be wise. there are voices at all price points within a short walk.

We are staying in Covent Garden. Years ago when we were there, they were redoing the station, so I don't know what the stairs are like there now. I LOVE all this advice. Thank you so much, everyone! Lots of references here to look up, which I will do now.