Switch type checking from mypy to Pyrefly (#8182)

[rosspeili]

Switch type checking from mypy to Pyrefly per 8182, also includes the check/typecheck rename/deprecation from 8225, can close once this lands.

1. Migrated [tool.mypy] with pyrefly init, then set monorepo search-path to match dev_tools/pypath.
2. Excluded notebooks (and generated cirq_google/cloud) as discussed on 8182.
3. Mapped mypy’s follow_imports=silent/skip third-party posture to ignore-missing-imports + replace-imports-with-any for sympy/networkx/pandas/protobuf.
4. Fixed two first-party issues similar to OpenFermion take (dtype is not None, cast before sorted for Qids).
5. Added check/typecheck, deprecated check/mypy (remove in v1.8), updated CI / check/all / shellcheck / deps / docs.

notes

• Left mypy-protobuf / --mypy_out alone (stub generation, not the typechecker CLI).
• Some Pyrefly error kinds that are much stricter than Cirq’s old silent-import mypy setup are disabled in [tool.pyrefly.errors] for this migration.

Test plan

• pyrefly check → 0 errors locally
• black / ruff clean on touched Python
• pytest on touched modules
• CI Type check job green

Fixes #8182

[rosspeili]

Config choices and follow-up

Since pyrefly is stricter than cirq’s previous mypy config (follow_imports=silent on sympy/networkx/pandas/protobuf), after mapping that to replace-imports-with-any, hundreds of first-party diagnostics remained (bad-argument-type, overload/kwargs patterns, etc.) that mypy did not effectively enforce. Per #8182 (“fix or adjust config for low-priority”), those kinds are disabled for now so the tool switch stays green without cirq-wide annotation rewrite.

Same idea as the OpenFermion pyrefly migration (#1433): migrate the checker first, tighten selectively later.

Suggested follow-up unless otherwise advised

1. Re-enable error kinds one at a time (start with bad-return / missing-attribute).
2. Fix or narrowly # type: ignore real first-party issues.
3. Prefer that over expanding replace-imports-with-any.

Happy to open that follow-ups after this lands, or adjust the disable list here if you’d rather tighten in this PR.

@pavoljuhas @mhucka, this also covers #8225’s check/typecheck / deprecate-check/mypy bits.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.60%. Comparing base (726eed6) to head (a488ffd).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #8227   +/-   ##
=======================================
  Coverage   99.60%   99.60%           
=======================================
  Files        1118     1118           
  Lines      101667   101667           
=======================================
  Hits       101261   101261           
  Misses        406      406           

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