[3.14] gh-91555: disable logger while handling log record (GH-131812) (GH-133899)

Prevent the possibility of re-entrancy leading to deadlock or infinite recursion (caused by logging triggered by logging), by disabling logging while the logger is handling log messages.
(cherry picked from commit 2561e148ec985755baa3984b91fd0bfc089b283c)

Co-authored-by: Duane Griffin <duaneg@dghda.com>