[3.13] Update the documentation howto index page and group docs into 3 logical sections (GH-119366, GH-120703) (GH-120646)

Update the documentation howto index page and group docs into 3 logical sections (GH-119366)

(cherry picked from commit a26d27e7ee512cd822b7a7ba075171152779ffdd)

Includes a follow-up fix to properly merge GH-119877:
* Add a link to free-threading HOWTO to the index (GH-120703)
  (cherry picked from commit 45d5cab533a607716b2b41134839a59facf309cd)

Co-authored-by: Carol Willing <carolcode@willingconsulting.com>
Co-authored-by: Ned Batchelder <ned@nedbatchelder.com>