refactor(backend): Clean Architecture layering

[GRACENOBLE]

Summary

• Replaces the flat internal/database + internal/server monolith with explicit Clean Architecture layers: domain → usecase → repository/postgres + handler → server
• HealthStats promoted from map[string]string to a typed struct with JSON tags
• Business logic (connection pool threshold messages) moved from the repository into the use case, where policy decisions belong
• HealthHandler exported for naming consistency with HelloWorldHandler
• NewServer() now returns (*http.Server, error) instead of panicking on DB failure
• All backend docs updated to reflect the new layout and patterns

Test plan

• go vet ./... passes (no output)
• make test passes unit tests (handler httptest)
• make itest passes integration tests against Testcontainers Postgres (requires Docker)
• GET / returns {"message":"Hello World"} with 200
• GET /health returns typed JSON stats with 200 when DB is up; 503 when DB is down

[coderabbitai]

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ℹ️ Review info

⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro

Run ID: bd87266d-f518-443c-86f4-9dc7f55e7dc5

📥 Commits

Reviewing files that changed from the base of the PR and between a9c6e2f and 396733e.

📒 Files selected for processing (24)

• CLAUDE.md
• backend/.env.example
• backend/Makefile
• backend/cmd/api/main.go
• backend/docs/_index.md
• backend/docs/database.md
• backend/docs/error-handling.md
• backend/docs/routing.md
• backend/docs/testing.md
• backend/internal/database/database.go
• backend/internal/database/database_test.go
• backend/internal/domain/health.go
• backend/internal/handler/handler.go
• backend/internal/handler/health_handler.go
• backend/internal/handler/hello_handler.go
• backend/internal/handler/hello_handler_test.go
• backend/internal/handler/routes.go
• backend/internal/repository/postgres/db.go
• backend/internal/repository/postgres/health_repository.go
• backend/internal/repository/postgres/health_repository_test.go
• backend/internal/server/routes.go
• backend/internal/server/server.go
• backend/internal/usecase/health_usecase.go
• web/app/page.tsx

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch backend-setup

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