If we take a reader lock, we can't call any functions that take a writer
lock internally without causing deadlocks once the reader lock is
actually enforced in the main thread, too. Take the reader lock only
where it is actually needed.

Signed-off-by: Kevin Wolf <kwolf@redhat.com>
Message-Id: <20230510203601.418015-5-kwolf@redhat.com>
Reviewed-by: Eric Blake <eblake@redhat.com>
Signed-off-by: Kevin Wolf <kwolf@redhat.com>