[vcpkg] Increment number of retries and timeout of fs.rename() (#13931)

* Fix retry logic for fs.rename()

* Increase timeout for fs.rename(), add diagnostic message

* Make formatting happy

* Exponential backoff for archive file rename

* Remove random local file from last commit

* Remove random local file from last commit

* Update toolsrc/src/vcpkg/archives.cpp

Co-authored-by: Mikayel Apozyan <Mikayel.Apozyan@avira.com>
Co-authored-by: nicole mazzuca <mazzucan@outlook.com>

toolsrc/src/vcpkg/archives.cpp

@@ -1,3 +1,4 @@
+#include <vcpkg/base/system.print.h>
 #include <vcpkg/base/system.process.h>
 
 #include <vcpkg/archives.h>
@@ -97,12 +98,16 @@ namespace vcpkg::Archives
 
         fs.rename(to_path_partial, to_path, ec);
 
-        for (int i = 0; i < 5 && ec; i++)
-        {
-            i++;
         using namespace std::chrono_literals;
-            std::this_thread::sleep_for(i * 100ms);
+
+        auto retry_delay = 8ms;
+
+        for (int i = 0; i < 10 && ec; i++)
+        {
+            using namespace std::chrono_literals;
+            std::this_thread::sleep_for(retry_delay);
             fs.rename(to_path_partial, to_path, ec);
+            retry_delay *= 2;
         }
 
         Checks::check_exit(VCPKG_LINE_INFO,