[FEATURE] Update context when moving Cowork task into project

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

I find myself often starting a Cowork task, only later realizing it actually belongs in a Cowork project. So I move the task into the project. But I noticed that when continuing the task, the task context is restricted to the initial task context (outside of the project), even though from that point outputs WILL be placed in the project output folder. I couldn't find any documentation on this. There is some documentation on moving a chat OUTSIDE of a project, but not vice versa.

Proposed Solution

Would be great to have the chat/task context 'resetted' when the task is moved into a project, and re-initialized with the first follow-up interaction inside the project.

Alternative Solutions

I guess an alternative would be to 'copy' the taks into a project, but only transferring the initial message so that the entire conversation can be re-started with project context, tools and mounts available. But that feels like a 'workaround', because you'll end up with two chats about the same project, one half underway but without relevant context and instruction, and one starting over with the project context.

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

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Additional Context

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