[ci] [docs] update some docs and CI dependencies

[jameslamb]

Proposes updating the following dependencies to their latest versions:

• libraries (and Python and R versions) used to create the docs hosted at https://lightgbm.readthedocs.io/en/latest/
• static analyzers like cpplint and mypy

Benefits of these changes

• faster conda environment solves = faster builds
• extends further into the future the time til we have to upgrade these language versions on readthedocs again

Notes for Reviewers

Even though the latest release of sphinx is the 7.x series, I'm proposing using sphinx>=6.0 because LightGBM'ss docs rely on breathe, and as of this writing the breathe conda-forge package has a ceiling of breathe<7.0.

• Sphinx 7.2 support breathe-doc/breathe#943
• https://github.com/conda-forge/breathe-feedstock/blob/5d9908bf915d15abbb4fe6d768a694f53e305d72/recipe/meta.yaml#L28

Despite that ceiling not being present for wheels on PyPI:

• Add Sphinx 6.1.3 to test matrix breathe-doc/breathe#885

# this happily installs breather 4.35 and sphinx 7.2.6 together
docker run \
  --rm \
  -it python:3.10 \
   /bin/bash -c "pip install 'breathe>=4.35' 'sphinx>7.0'"

[borchero]

LGTM :)