Remove use of AsyncLocal to track Task input_required status #1185
Description
Do we really need to use the execution context to track the automatic status updates? Any request would be made via the request context. It also seems weird to me that this PR doesn't make any changes to McpSessionHandler. I figured a lot of the task handling would be the same for the client and server, so it makes sense for the logic tracking related requests to go there.
Originally posted by @halter73 in #1170 (comment)