I, too, have been thinking about this so my answer is from someone who hasn't visited Edinburgh since 2018 and then not with people who were big walkers. I'm going in June.
I saw a very good thread on Trip Advisor the other day with some geological information I knew (about the Castle being perched atop the volcanic core) and some I'd not come across before (hadn't looked either, lol!)
"Edinburgh Castle is perched atop a volcanic core, and the Royal mile stretches eastwards - crag and tail - down to Holyrood. To the north, again west to east, you had the Nor' Loch in a glacially sculpted trench. Now dried out, it contains Waverley Station and the railtrack from Glasgow. Beyond that the rolling ridge on which the New Town was founded."
Look at reply #5:
https://www.tripadvisor.com/ShowTopic-g186525-i108-k15332251-Need_Info_on_2_Walking_Routes_N_of_Waverly_Station-Edinburgh_Scotland.html
So, it looks like Market Street is on the south edge of the "glacially sculpted trench", so up to the Royal Mile but not sure how far down you'll have to go for the Princess Gardens, Princes St and then up to New Town for Dean Village.
I've been looking at some walking routes which include some of the stairs or AVOIDS some of the stairs, lol and have decided I will just have to see what's what when I get there.