Support MCP client session resumption (sessionId reuse) in Python SDK

Description

Summary

The Python MCP SDK currently appears to create a new session whenever a client is instantiated. It would be valuable to support resuming an existing MCP session using a previously issued sessionId, similar to functionality discussed and addressed in the C# SDK (see modelcontextprotocol/csharp-sdk#946).

This would enable persistent and stateful workflows in agent-based systems.

Problem

At present, there does not appear to be a documented way in the Python SDK to:

• Reuse an existing sessionId
• Resume a previously established MCP session
• Control session lifecycle independently of the client object's lifetime

Why This Is Important

• In agent-driven architectures , session continuity allows:
• More efficient orchestration
• Reduced overhead from repeated session initialization

As MCP adoption grows across SDKs (C#, TypeScript, Python), having consistent session lifecycle capabilities improves cross-language parity and developer experience.

References

https://github.com/modelcontextprotocol/csharp-sdk/issues/946

Start by tracing how the Python SDK creates and manages client sessions, then review the linked C# SDK issue for the session-resumption context. Done should include a supported way to reuse a previously issued sessionId, resume a session independently of client lifetime, and document the behavior.