[3.12] gh-108303: Move all doctest related files and tests to `Lib/test/test_doctest/` (GH-112109) (#114254)

gh-108303: Move all doctest related files and tests to `Lib/test/test_doctest/` (GH-112109)
(cherry picked from commit 9c93350f582fe6f5fed2cd873869dfe4fbf2dfe8)

Co-authored-by: Nikita Sobolev <mail@sobolevn.me>
Co-authored-by: Brett Cannon <brett@python.org>