Simplify logging code in flutter_driver (#45945)

* Simplify logging code in flutter_driver

It appears nobody is benefitting from this logic, so we may as well not pay the cost.

* Make all of the driver interface public.

This is the second attempt at this; it should be better than before because the Logger interface, which conflicted in various places, no longer exists.

See #45733 for original attempt.

This reverts commit 0ce9206ef457fcd59b203544244a9bedf0a9ac31 (PR #45924).