Context

Investigated whether ty's unused-awaitable rule catches missing
{{await}}s that mypy's strict config misses (full write-up:
https://gist.github.com/blink1073/a9fe43fbb2643b12ab4472836e77ee40). It found 2 real
bugs, fixed separately in PYTHON-5975, plus 14 expected false positives from the
@require_sync convention. mypy's own unused-coroutine check misses these
because no-untyped-def is disabled for test code. This ticket wires up ty as an
ongoing check so future missing-awaits are caught automatically.

Definition of done

* ty check --ignore all --error unused-awaitable wired up as a just recipe
and in CI/pre-commit, scoped to pymongo, gridfs, bson, test
* The 14 known @require_sync false positives suppressed without changing their
behavior
* Check passes clean

Pitfalls

* ty isn't a project dependency yet; decide between uvx ty (no pin) or
adding it to a dependency group
* Keep the check scoped to unused-awaitable. The related invalid-await rule
also fired, including in real source, but overlaps with existing
type: ignore[misc] suppressions and needs separate verification (out of scope)
* Don't suppress the 14 @require_sync false positives by adding await;
that's intentional dead code matching the generated sync test file