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
(cherry picked from commit 3c3f211d1e5698da6eea9e83584acb2dee4ca46e)
diff --git a/common.h b/common.h
index de536fd..3dc36a9 100644
--- a/common.h
+++ b/common.h
@@ -27,7 +27,9 @@
 static constexpr int kRecoveryApiVersion = 3;
 
 class RecoveryUI;
+struct selabel_handle;
 
+extern struct selabel_handle* sehandle;
 extern RecoveryUI* ui;
 extern bool modified_flash;
 
@@ -37,13 +39,6 @@
 // The reason argument provided in "--reason=".
 extern const char* reason;
 
-// fopen(3)'s the given file, by mounting volumes and making parent dirs as necessary. Returns the
-// file pointer, or nullptr on error.
-FILE* fopen_path(const std::string& path, const char* mode);
-
-// In turn fflush(3)'s, fsync(3)'s and fclose(3)'s the given stream.
-void check_and_fclose(FILE* fp, const std::string& name);
-
 void ui_print(const char* format, ...) __printflike(1, 2);
 
 bool is_ro_debuggable();