Refactors calendar initialization with factory

Implements a factory pattern for manager creation and
initialization, improving dependency management and
extensibility.

This change replaces direct manager instantiation with a
`ManagerFactory` that handles dependency injection. This
enhances code organization and testability. It also includes
an initialization sequence diagram for better understanding
of the calendar's architecture and data flow.

.claude/settings.local.json

@@ -5,7 +5,8 @@
       "Bash(npm run build:*)",
       "Bash(powershell:*)",
       "Bash(rg:*)",
-      "Bash(find:*)"
+      "Bash(find:*)",
+      "Bash(mv:*)"
     ],
     "deny": []
   }