Although not every manga has the author(s) drawing depictions of themselves, many do and I have yet to come across an example where it was anything other than the ‘chibi’ or superdeformed style of drawing when it was supposed to be a human face.
Anthropomorphic animals, non-human avatars, masks, and so on are also popular.
Sometimes it becomes so exaggerated it seems silly and intentionally self-demeaning.
Clearly it’s an established trope, or standard, by now but why?