Update MWLoggerMonologHandler for Monolog 1.12.0

Update MWLoggerMonologHandler for Monolog 1.12.0

Monolog 1.12.0 "fixed" Handler::isHandling() so that instead of a full
log record it is only passed an array with the log event's level.
MWLoggerMonologHandler was relying on a full record to allow inspecting
the channel name and looking for a 'private' flag in the context
information.

Update MWLoggerMonologHandler to do legacy processing checks in
Handler::write() where the full log event is present for inspection.

Bug: T89313
Change-Id: Ia878c2cb6bff47d6b35ff38ba3b7ac2ea5556565