[3.10] gh-95432: Add doctests for the sqlite3 docs (GH-96225) (#96379)

As a consequence of the added test, this commit also includes
fixes for broken examples.

- Add separate namespace for trace tests bco. module level callback
- Move more backup and cursor examples under separate namespaces.
(cherry picked from commit bf9259776dff5348bc854983409ea68618c1f174)

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