fish_private_mode is active if set to something non-empty, but the docs
suggested checking if it is set at all. Switch the docs to match the
implementation through `test -n "$fish_private_mode"`
Fixes#8001
This breaks apart the massive "index" document into
1. An "index" document that explains how to install and set up fish
and links to the other documents
2. A "fish-language" document that describes the syntax and semantics
of the language
3. A "fish-interactive" document that describes how to use fish
interactively
No change to the content has been made, only the parts have been moved
from index and some of the formatting (links and header levels) were
fixed.
See #7348.
