Halve the time to build docs locally by inlining spell checking - #74549

Previously to see the same error in docs build as you would get in CI,
you would have to run both the docs build and the spellchecking build.

The issue was that the spellcheck (using sphinx-contrib's spelling) was
defined as a new builder, meaning you could either build HTML, or you
can check spelling. On CI, this didn't result in any extra wall-clock
time as the jobs were parallelized (but this change does remove a job
from the overall matrix), but locally that was almost always not the
case, so this would mean full build to view the HTML, and spell checking
build to look for errors, resulting in it taking twice as long.

The upstream spellchecker was also slower than it should be mainly
because its importable-module filter calls find_spec on every distinct
identifier-like word before consulting the dictionary. Here it runs only
for words that are still misspelled. Word lists, filters and
:spelling:ignore: behave as before.

This also handles errors a lot more nicely (hence all the code deletions):

• They are written natively to a JSON file, not scraped from a stream
• They also show up as GH annotations (Where we can attribute it to a
  real file) to make fixing them easier on PRs.

Please note: this is lightly breaking for Airflow contributors as
breeze build-docs --docs-only and --spellcheck-only are gone --
every build checks spelling now as it is essentially free (on the order
of milliseconds per module).

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