The only other verb I’ve heard is keyboarding, and this is only used in reference to the class, or otherwise learning how to use a computer keyboard.
Otherwise, I use write or type, not that I’ve used a pen or pencil or typewriter in a long time.
BTW, the whole meaning of typewriter is something that writes type. Type is just another way of referring to printed words, even when printed on a screen.
ETA:
I only call it editing if I’ve already written something before. You write, then you edit/proofread.
But a type writer is a machine you use to write type (“printed letters” as opposed to longhand); “type” is a root for the word typewriter, an abbreviation for it, and the result of typing on a typewriter or a computer. Whether you’re using a typewriter that’s good only for typing or good for other things as well, the end result is typed text. My boss has a fancy laptop he can write on with a stylus: when he uses the stylus, he is not getting typed letters but ugly scribbles, he is not typing.
Fun fact: in Italian, the first typewriters were referred to as cembalo scrivano, “scribe-harpsichord,” which is the best technical term ever conceived.
In the word processing field, we used to use the “input” as a noun for a job that is mainly text to be typed for the first for the first time, as opposed to revisions, etc.
So maybe “input” could be the noun used in response to the OP since whatever you’re using (the keyboard/stylus/voice recognition), etc. to get to where you want to go, it ends up being put into a document or field or message board forum and, that word doesn’t have to take into account the medium (software, hardware) that comes between inputting and the final result of that.
I don’t see why “type” shouldn’t be used; to my mind it’s even less of a problem than saying you “dial” a number (which isn’t a problem either), since the physical action is exactly the same whether you’re typing on a typewriter or on a computer keyboard (minus a bit of brute force and disentangling little metal bars from each other).