[3.8] bpo-41028: Doc: Move switchers to docsbuild-scripts. (GH-20969)

[miss-islington]

(cherry picked from commit ee2549c)

Co-authored-by: Julien Palard julien@palard.fr

https://bugs.python.org/issue41028

[miss-islington]

@JulienPalard: Status check is done, and it's a success ✅ .

[ned-deily]

This should be backported so that the documentation built and archived for subsequent 3.8.x releases has the new generic "Docs by version" index sidebar, rather than the old out-of-date version specific one. (The current 3.8 on-line docs are already being fixed up by the docsbuild process however security branch docs are only rebuilt manually.)

[miss-islington]

@JulienPalard: Status check is done, and it's a success ✅ .

[vstinner]

@ambv: Would you mind to merge this change into the 3.8 branch? See @ned-deily's comment.