docs(site): refine index.md homepage layout

- cleaned up front matter format
- improved Quick Start with clearer commands
- added GitHub badge and direct README reference
- ensured Adoption Guides are properly linked

Author: barissayli

docs/index.md

@@ -1,15 +1,16 @@
 ---
+
 layout: default
 title: Home
 nav_order: 1
----
+------------
 
 # Spring Boot OpenAPI Generics Clients
 
 Welcome! 👋
 
-This site is generated from the [
-`spring-boot-openapi-generics-clients`](https://github.com/bsayli/spring-boot-openapi-generics-clients) repository.
+This site is generated from the
+[`spring-boot-openapi-generics-clients`](https://github.com/bsayli/spring-boot-openapi-generics-clients) repository.
 
 ---
 
@@ -23,11 +24,11 @@ This site is generated from the [
 ## 🚀 Quick Start
 
 ```bash
-cd customer-service
-mvn spring-boot:run
+# Run the sample server
+cd customer-service && mvn spring-boot:run
 
-cd ../customer-service-client
-mvn clean install
+# Generate and build the client
+cd ../customer-service-client && mvn clean install
 ```
 
 Generated wrappers can be found under:
@@ -38,4 +39,6 @@ Generated wrappers can be found under:
 
 ## 📖 More Docs
 
-See the full [README on GitHub](https://github.com/bsayli/spring-boot-openapi-generics-clients#readme).
+[![View on GitHub](https://img.shields.io/badge/GitHub-View%20Repo-blue?logo=github)](https://github.com/bsayli/spring-boot-openapi-generics-clients)
+
+See the full [README on GitHub](https://github.com/bsayli/spring-boot-openapi-generics-clients#readme).