[3.13] gh-121615: Improve `module.rst` C-API docs with better error descriptions (GH-121616) (#121618)

gh-121615: Improve `module.rst` C-API docs with better error descriptions (GH-121616)
(cherry picked from commit e6264b44dc7221c713b14dfa0f5929b33d362829)

Co-authored-by: sobolevn <mail@sobolevn.me>