I am currently evaluating the use of the login/password_downwards_compatibility
parameter, but I can not fully understand it.
In what cases is it used? And what risks would it have associated?
What exactly don't you understand in official documentation for this parameter?
Values from 0 to 5 shows strictness of SAP password hash generation and evaluation during logon, starting from the most strict (0) to the most legacy way (5).
You do not need to change the default value (aka 1) of the parameter unless:
You must not touch this parameter at all unless you are a professional BASIS. Period.