[clang-tidy] Organize test files into subdirectories by module (NFC)

Eliminate clutter by reorganizing the Lit test files for clang-tidy:
- Move checkers/<module>-* to checkers/<module>/*.
- Move module specific inputs from Inputs to <module>/Inputs.  Remove
  any module prefix from the file or subdirectory name as they are no
  longer needed.
- Introduce a Lit substitution %clang_tidy_headers for the system
  headers in checkers/Inputs/Headers and use this throughout.  This
  avoids referencing system headers through a relative path to the
  parent directory and makes it clear that these fake system headers are
  shared among all modules.
- Update add_new_check.py to follow the above conventions when creating
  the boiler plate test files for a new check.
- Update Contributing.rst to describe per-module Inputs directory and
  fix link to test source code.

Differential Revision: https://reviews.llvm.org/D128072