Introduce server sessions

[tiginamaria]

Introduce a ServerSession to manage multiple connections to the mcp server. Protocall logic of the Server was moved to ServerSession, while MCP resources logic remained in Server

Motivation and Context

1. Fix the multiple connection issues reported for sse transport
2. Avoid server duplications during configurations, now every connection creates a session, but the server stays single

How Has This Been Tested?

Added SseIntegrationTest and WebSocketIntegrationTest integration tests to check connection with single and multiple clients

Breaking Changes

This change caused several depreciations:

1. The Server -> Protocol inheritance (which caused single connection issue) should be removed in future releases, now, all the methods inherited from Protocall marked as Deprecated with a Warning
2. Websocket ktor server initialization changes in order not to create server instance per connection

Types of changes

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

Checklist

• I have read the MCP Documentation
• 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

[tiginamaria]

Finishes without await in tests, not sure if it's a right approach to fix it, please take a look here! Really need some help here

[devcrocod]

The PR looks good to me overall!

Please take a look at my comments.
My main concern is about the behavior of the Server
It would also be great to update the existing samples and the README accordingly

[Copilot]

Pull Request Overview

This PR introduces server sessions to manage multiple connections to MCP servers. The implementation moves protocol logic from the Server class to a new ServerSession class, allowing the server to handle multiple simultaneous connections while maintaining a single server instance.

• Introduces ServerSession class for managing individual client connections
• Moves protocol-level functionality from Server to ServerSession
• Updates WebSocket and SSE transport implementations to support multiple sessions
• Adds comprehensive integration tests for both single and multiple connection scenarios

Reviewed Changes

Copilot reviewed 16 out of 16 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
SseIntegrationTest.kt	New integration test verifying SSE transport with single and multiple client connections
WebSocketIntegrationTest.kt	New integration test verifying WebSocket transport with single and multiple client connections
SseTransportTest.kt	Updates to use new SseTransportManager instead of direct transport map
WebSocketMcpTransport.kt	Adds debug logging for WebSocket transport operations
Protocol.kt	Refactors logger variable naming for consistency
WebSocketMcpServerTransport.kt	Adds debug logging for session header validation
WebSocketMcpKtorServerExtensions.kt	Major refactor to support session-based architecture with new API and deprecation warnings
ServerSession.kt	New class implementing session-specific protocol handling moved from Server
Server.kt	Refactored to manage multiple sessions while maintaining resource management
SSEServerTransport.kt	Removes unused import
KtorServer.kt	Introduces SseTransportManager for better session management
WebSocketMcpKtorClientExtensions.kt	Adds debug logging for client connection process
WebSocketClientTransport.kt	Adds debug logging for session initialization
SSEClientTransport.kt	Adds debug logging for message sending and endpoint connection
Client.kt	Improves error handling during connection initialization
kotlin-sdk.api	Updates API surface to include new classes and deprecation warnings

Comments suppressed due to low confidence (1)

src/commonTest/kotlin/io/modelcontextprotocol/kotlin/sdk/integration/WebSocketIntegrationTest.kt:37

• The test method name 'client should be able to connect to websocket server 2' is unclear. The '2' suffix doesn't indicate what distinguishes this test from others. Consider renaming to something more descriptive like 'client establishes websocket connection successfully'.

    fun `client should be able to connect to websocket server 2`() = runTest {

[e5l]

Hey @tiginamaria, thank you for the PR. Could you add a sample as a docs page illustrating what the difference will be between kotlin and the original TypeScript API?