recovery: Refactor logging code into logging.cpp

Move common logging related functions to
rotate_logs.cpp, and rename that to logging.cpp.

Test: Recovery works
Bug: 78793464
Change-Id: I00f20a79a296680122b8437d54a87897c5cb2fc7
diff --git a/recovery_main.cpp b/recovery_main.cpp
index 9f579f7..3147511 100644
--- a/recovery_main.cpp
+++ b/recovery_main.cpp
@@ -24,10 +24,10 @@
 #include <private/android_logger.h> /* private pmsg functions */
 
 #include "common.h"
+#include "logging.h"
 #include "minadbd/minadbd.h"
 #include "otautil/paths.h"
 #include "private/recovery.h"
-#include "rotate_logs.h"
 #include "ui.h"
 
 static void UiLogger(android::base::LogId /* id */, android::base::LogSeverity severity,