Context

When we pinned the compatible version of pymongo to ~4.9 in MOTOR-1351, it had the unintended affect of making it hard to have an application that depends on both pymongo and motor. An example given by user MohammedShokr is:

Because no versions of motor match >3.6.1,<4.0.0
and motor (3.6.1) depends on pymongo (>=4.9,<4.10), motor (>=3.6.1,<4.0.0) requires pymongo (>=4.9,<4.10).
And because my-x-package (x.x.x) depends on pymongo (4.10.1),

We did the bulk of the work required to support the async refactor of PyMongo in MOTOR-1353, so it shouldn't be too much more work to support newer versions.

Definition of done

Update our support to include PyMongo 4.10 and the upcoming PyMongo 4.11.

Pitfalls

We may need to remain fixed to one minor version of PyMongo at a time moving forward until Motor is fully sunset, depending on how much the internal APIs of PyMongo change.