[3.13] GH-121970: Use Ruff to check and format the docs tools (GH-122018) (#122023)

GH-121970: Use Ruff to check and format the docs tools (GH-122018)
(cherry picked from commit 40855f3ab80ced9950c725b710f507c0e903b70a)

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