elpy don't syntax check on the fly

[c . buhtz]

I have Windows 10, running "GNU Emacs 27.1 (build 1, i686-w64-mingw32) 
of 2020-08-21".

I used this (not perfect) tutorial to setup emacs.
https://realpython.com/emacs-the-best-python-editor/

I learned that installing "elpy" from melpa (via emacs) is not enough. 
"elpy" uses external commandline tools (e.g. flake8) - but very 
intransparent to the user. Even the official documentation is not clear 
about that part.
https://elpy.readthedocs.io/_/downloads/en/latest/pdf/
The documentation only offers a name. No URL to a project side or bug 
tracker nor an email.

I do not want to neg here. I want to learn how to do my stuff AND how to 
improve the project/community. So a side-question: What would be the 
usual way to find the project website for an emacs-mode and open a 
ticket?

Ok, back to the main problem.

I explicite installed flake8 via pip. It works because C-c C-v does show 
my expected syntax errors.
But the tutorial I first mentioned here tells me elpy should show me 
syntax errors on the fly/live while I am typing. But it does not.

How can I go on with diagnosis in that case?
The elpy doc tells me the syntax checking only happens when the file is 
saved.
But the tutorial indicates that it happens on the fly. I am confused.

Is there an alternative to have a real on the fly syntax checking while 
typing?