[3.10] gh-93738: Disallow pre-v3 syntax in the C domain (GH-97962) (#97977)

Also, disable using invalid sphinx-lint 0.6.2.
(cherry picked from commit f612565bd32d4ab0945798da775eea070f08b6fe)

Co-authored-by: Adam Turner <9087854+AA-Turner@users.noreply.github.com>