Keep an eye on pytest-playwright updates

[rebeccacremona]

pytest-playwright uses the https://pyee.readthedocs.io/en/latest/index.html library for managing some of it's async and async-adjacent aspects. We should revisit this periodically to see if we can get rid of this after an update.

Originally posted by @holtchesley in https://github.com/harvard-lil/perma/pull/3023#discussion_r796675241