ci: cache mypy incremental state in Backend Type Check

[corrin]

Backend Type Check ran full-strict mypy cold on every push (~2m15s across recent runs). Mypy is incremental by design, so this restores .mypy_cache before the gate: typical pushes re-check only the modules whose dependencies changed, dropping the job to tens of seconds.

Cache mechanics: actions/cache never overwrites an existing key, so the key embeds the commit SHA (every run saves a fresh snapshot) and restore-keys falls back to the newest snapshot for the same poetry.lock + pyproject.toml. A deps or mypy-config change misses the fallback and does one cold run, exactly as today. Same pinned actions/cache SHA as the existing Poetry cache steps.

Investigated and rejected while here: caching ~/.cache/pre-commit — pre-commit/action@v3 already does that internally (verified in its action.yml), so the Pre-commit job's ~3m40s is genuine hook execution. Backend Tests' ~6m is real test execution; the lever there would be --parallel, deliberately not bundled into this change.

First run on this PR is the cold seed; the speedup shows from the next push onward.

🤖 Generated with Claude Code

https://claude.ai/code/session_01PnuHL7w3UisSk6KQ81q3Qf

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