[3.11] gh-95273: Reorganize sqlite3 doc module level funcs and vars (GH-95626) (#95801)

Co-authored-by: Ezio Melotti <ezio.melotti@gmail.com>
Co-authored-by: CAM Gerlach <CAM.Gerlach@Gerlach.CAM>.
(cherry picked from commit 41c939cb35cda395388a775156c367676efffebe)

Co-authored-by: Erlend E. Aasland <erlend.aasland@protonmail.com>