Add integration tests for main API flows

Add integration tests that spin up the Express app against a test database and exercise key flows including creating an application, updating status, adding notes, and listing with filters and pagination.

Look for existing test setup and database configuration. The integration tests need to start the Express app, connect to a test database, and simulate API calls for creating applications, updating status, adding notes, and listing with filters/pagination. Check for test utilities or a `test` directory to understand the framework. Running existing tests will show the pattern. 'Done' means the key flows pass in an integrated environment.

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