> There are both case-fold-search and its isearch-specific counterpart
> isearch-case-fold-search, so maybe both char-fold-search and
> isearch-char-fold-search should exist.

Actually, `isearch-case-fold-search' is an internal variable and
configuring it has no effect. If you want configure isearch's case-folding,
you have to use the general `case-fold-search'.

That is why there's no isearch-char-fold-search.