[Question] Implementing background tasks via MCP servers

Hi,

Currently within a session it appears that Claude Code processes each tool call sequentially. I am wondering, is there a way to issue a long running tool call request, continue the conversation, and then accept the tool call response whenever it is ready? I was thinking that using MCP servers via SSE transport might be a way to do this, but it's not clear to me that Claude Code can handle this.

This use case is my motivation: https://github.com/stagewise-io/stagewise/pull/182#issuecomment-2949901304

Essentially, we want to be able to inject context from an external event, without explicitly having the request/response.

Thank you!