Title is pretty much everything!
I have these high up windows that I'd like to clean and maybe in the future install curtains on. I guestimate the wall being 20ft (6m) tall.
For other rooms in the house I typically use an A-Frame, but it's impossible to find an A-Frame to reach that high where I am.
I plan on draping a towel over the top of the ladder to prevent scratches and scuffs on the wall, as well as getting a rubber mat or something if the floor seems slippery. I am just not sure if drywall would support a ladder? Especially near the frame of the windows. Maybe there's something else I'm not considering as well?
Make sure to follow the 4-to-1 rule - for every 4' of climb, the base should be 1' from the wall.
You should be fine. Ideally, you'd tie the ladder off to something, or have the top extend 3' above the surface it's against (like if you're using it to get to a roof). Obviously neither of those really apply here. I'm an electrician and we have to do stuff like this pretty often.
As for the strength of the wall around the windows, those should be framed in, meaning there are extra 2x4s around them. Try to extend the ladder higher than you need to be so you're not on the very top of it and you'll be alright