anon adverb archaic or informal: soon; shortly: I'll see you anon. ORIGIN Old English on ān‘into one’, on āne‘in one’. The original sense was ‘in or into one state, course, etc.’, which developed into the temporal sense ‘at once’.
When characters in Shakespeare’s plays said anon, they meant at once. It doesn’t mean that any more, in this case not because the word changed but because people’s behaviour and our recognition of it changed. We all get busy with other things or we procrastinate. Anyway, anon became later.
Anon is also short for anonymous. Virginia Woolf said she thought that Anonymous was a woman. Not quite what she said…”I would venture to guess that Anon, who wrote so many poems without signing them, was often a woman.” Very often misquoted as "For most of history, Anonymous was a woman." Wikipedia
I use it all the time, as you know. To me, it means, have a little patience. I’ll get to it. I will. I’ll try.