[clang-tidy] Make readability-string-compare check use <string> header

Improve the generic <string> header by adding another constructor,
std::basic_string::empty and operator!= overload set so that it can be
used to replace the custom implementation in the
readability-string-compare check.

Depends on D145311

Reviewed By: PiotrZSL

Differential Revision: https://reviews.llvm.org/D145312