Enhanced sqlite3 connection context management documentation with contextlib.closing gh-109234 (#109322)

* Enhanced sqlite3 connection context management documentation with contextlib.closing

* 📜🤖 Added by blurb_it.

* Fixed gitignore spelling error from nitignore to gitignore

* Renamed .gitignore to .nitignore

* Added generated doctests

* Deleted sqlite3 generated files

* Removed white-space changes

* Removed News entry from the doc

* Expanded a note that context manager can be used for connection management using contextlib.closing

* Removed repeated contextlib.closing code snippet

* Expanded the note around usage of context manageer for sqlite3 connection management

* Deleted extra white-spaces

* Deleted extra white-space

* re-arranged context manager wording

* Re-arranged word layout on how to use context manager

* Fix whitespace errors

* Remove unneeded change in .gitignore

* Added suggested changes

* Added suggested change redirecting to the contextlib.closing implementation

* Added closing keyword

* Removed line 2473

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Co-authored-by: blurb-it[bot] <43283697+blurb-it[bot]@users.noreply.github.com>
Co-authored-by: Erlend E. Aasland <erlend@python.org>