Refactor to JSON API with Chi router and interface-based design

- Add pkg/greet/api_v1.go with ApiV1Greet interface and handler
- Implement Greeter interface for dependency injection
- Return JSON responses with proper Content-Type headers
- Move greet service instantiation to server package
- Separate v1 route registration into registerApiV1Routes function
- Health endpoint at /api level, greet endpoints at /api/v1/greet
- Simplify server entrypoint by removing external dependencies

go.mod

@@ -1,3 +1,5 @@
 module DanceLessonsCoach
 
 go 1.26.1
+
+require github.com/go-chi/chi/v5 v5.2.5 // indirect