fix(ci): build the docs gate from scratch, so a local run cannot undercount

[breimanntools]

The docs gate built into docs/_build/gate, which persists. Sphinx is incremental, so a second run into the same directory re-read only the changed pages and every message from an untouched page was missing from the log.

Caught on a real branch: the first run reported 167 critical, the second reported 89 and printed

IMPROVED: 89 critical < baseline 167 (-78). Lower the baseline to 89.

— inviting a committed baseline that CI, which always builds a fresh checkout, would immediately exceed. The ratchet would then fail on master for a reason nobody could reproduce locally.

The fix

The build goes into a fresh temporary directory, discarded afterwards, so a local run always measures a full build and agrees with CI.

Verified: two consecutive runs on the same tree now both report 167 critical / 341 warning, where the second previously reported 89 / 62.

The IMPROVED message no longer names a number to commit either — a local build can legitimately differ from CI (an offline runner cannot reach the intersphinx inventories), so it now says to take the count from a CI run. A new test pins that.

27 tests in tests/unit/api_tests/test_check_docs_build.py pass.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.39%. Comparing base (3c11c90) to head (bf44fdf).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #585   +/-   ##
=======================================
  Coverage   95.39%   95.39%           
=======================================
  Files         222      222           
  Lines       23387    23387           
  Branches     4073     4073           
=======================================
  Hits        22309    22309           
  Misses        631      631           
  Partials      447      447           

Components	Coverage Δ
cpp_core	95.97% <ø> (ø)

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