fix!: Migrate Ktor extension functions from Routing to Route (#237) (#531)

# Migrate Ktor extension functions from `Routing` to `Route` (#237)

- Replaced `Routing` with `Route` in MCP-related functions for better
composability in nested contexts.
- Updated tests to verify compatibility with nested routes and subpaths.
- Deprecated legacy signatures and removed redundant overloads.

## How Has This Been Tested?
Unit test

## Breaking Changes
`Routing.mcp(...) `extension was replaced with `Route.mcp(...)`

## Types of changes

- [X] Bug fix (non-breaking change which fixes an issue)
- [ ] New feature (non-breaking change which adds functionality)
- [x] Breaking change (fix or feature that would cause existing
functionality to change)
- [ ] Documentation update

## Checklist
<!-- Go over all the following points, and put an `x` in all the boxes
that apply. -->
- [x] I have read the [MCP
Documentation](https://modelcontextprotocol.io)
- [x] My code follows the repository's style guidelines
- [ ] New and existing tests pass locally
- [ ] I have added appropriate error handling
- [ ] I have added or updated documentation as needed

## Additional context
Based on #314 by @IainHull but that PR is too outdated.

integration-test/src/jvmTest/kotlin/io/modelcontextprotocol/kotlin/sdk/integration/kotlin/KotlinTestBase.kt

@@ -8,10 +8,6 @@ import io.ktor.server.application.install
 import io.ktor.server.engine.EmbeddedServer
 import io.ktor.server.engine.embeddedServer
 import io.ktor.server.plugins.contentnegotiation.ContentNegotiation
-import io.ktor.server.routing.delete
-import io.ktor.server.routing.get
-import io.ktor.server.routing.post
-import io.ktor.server.routing.route
 import io.ktor.server.routing.routing
 import io.modelcontextprotocol.kotlin.sdk.client.Client
 import io.modelcontextprotocol.kotlin.sdk.client.SseClientTransport
@@ -22,6 +18,7 @@ import io.modelcontextprotocol.kotlin.sdk.server.ServerOptions
 import io.modelcontextprotocol.kotlin.sdk.server.StdioServerTransport
 import io.modelcontextprotocol.kotlin.sdk.server.StreamableHttpServerTransport
 import io.modelcontextprotocol.kotlin.sdk.server.mcp
+import io.modelcontextprotocol.kotlin.sdk.server.mcpStreamableHttp
 import io.modelcontextprotocol.kotlin.sdk.types.Implementation
 import io.modelcontextprotocol.kotlin.sdk.types.McpJson
 import io.modelcontextprotocol.kotlin.sdk.types.ServerCapabilities
@@ -54,6 +51,7 @@ abstract class KotlinTestBase {
 
     // Transport selection
     protected enum class TransportKind { SSE, STDIO, STREAMABLE_HTTP }
+
     protected open val transportKind: TransportKind = TransportKind.STDIO
 
     // STDIO-specific fields
@@ -168,19 +166,7 @@ abstract class KotlinTestBase {
                     install(ContentNegotiation) {
                         json(McpJson)
                     }
-                    routing {
-                        route("/mcp") {
-                            post {
-                                transport.handlePostRequest(null, call)
-                            }
-                            get {
-                                transport.handleGetRequest(null, call)
-                            }
-                            delete {
-                                transport.handleDeleteRequest(call)
-                            }
-                        }
-                    }
+                    mcpStreamableHttp(path = "/mcp") { server }
                 }.start(wait = false)
             }