feat: implement branded discord embeds and versioning

.agent/work/tickets/005-refactor-exam-logic.md

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+### Context & Goal
+
+The `exam` command currently contains a lot of business logic, including reward calculations, timer management, and complex database transactions. Moving this logic to a dedicated `ExamService` will improve testability, maintainability, and keep the command file focused on user interaction.
+
+### Dependencies
+
+- None
+
+### Affected Files
+
+- `shared/modules/economy/exam.service.ts`: New file for the exam logic.
+- `bot/commands/economy/exam.ts`: Refactor to use the new service.
+
+### Technical Constraints & Strategy
+
+- Implementation: Create an `ExamService` that handles `getExamStatus`, `takeExam`, and `registerForExam`.
+- The command should only handle user input and formatting the response embeds based on the service's result.
+- Ensure the Drizzle transactions are correctly handled within the service.
+
+### Definition of Done (Binary)
+
+- [ ] `ExamService` implemented with methods for all exam-related operations.
+- [ ] `bot/commands/economy/exam.ts` refactored to use the service.
+- [ ] Logic is covered by unit tests in a new test file.
+- [ ] Manual verification shows the exam command still works as expected.
+
+### New Test Files
+
+- `shared/modules/economy/exam.service.test.ts`: Unit tests for reward calculations and state transitions.