105 Add Authentication Check to Projects Routes

[bhuvanh66]

ℹ️ Issue

Closes #105

📝 Description

Added authentication to the projects lambda to protect its endpoints from unauthorized access. Without this, anyone with the URL could read or create projects once the lambda is made public.

Briefly list the changes made to the code:

1. Created auth.ts to verify Cognito JWTs and load the matching user from the database
2. Updated handler.ts to authenticate every request before running any route logic
3. Updated both test files to mock authentication so tests call handler directly instead of the live endpoint

✔️ Verification

Clone the branch and run npx jest from apps/backend/lambdas/projects
All tests should pass without a running Cognito instance since auth is mocked