On Windows, user.home maps to %USERPROFILE% environment variable, what is typically C:\Users\username.
There's no equivalent constant for that in Inno Setup. Probably because you are not supposed to store any files there. You should store your files to C:\Users\username\AppData\Roaming\app (or ...\Local\app). In Inno Setup that is {userappdata}\app (or {localappdata}\app). It Java, you can use System.getenv("APPDATA") (or System.getenv("LOCALAPPDATA")).
Anyway, to answer your question, you can use {%USERPROFILE}.
See also Inno Setup User Home Path.
Also in general, it's a bad idea to try to access a user profile in Inno Setup (un)installer, as the (un)installer can be executed using a different local account (typically Administrator), than the one you are interested in.
This is covered in Installing application for currently logged in user from Inno Setup installer running as Administrator.