Prepare for removing app access to some MessageQueue internals

MessageQueue's mMessages and next() are used by reflection
in some tests. There is now a public alternative.

Update the @UnsupportedAppUsage annotation to note our
intention to remove app access.
Reference TestLooperManager as the alternative.

go/new-mq-appcompat

Bug: 379472827
Flag: EXEMPT Javadoc
Change-Id: I1bf8d54b8f3eafc375da3b198c2c661bf5226fb4