GUI: user-initiated parallel task spawning without interrupting current turn

Problem

During a session, the user often observes things worth spinning off into a separate task (a bug to fix, a related refactor, etc.). Today the only way to do this is:

1. Type a message into the chat — but this interrupts the current turn, redirecting the assistant's train of thought.
2. Wait until the assistant finishes, then ask it to spawn_task — but by then the observation may be forgotten or the moment has passed.
3. Manually open a new session from the sidebar — but you lose the current session's context.

The assistant has spawn_task (the chip affordance) to flag out-of-scope work into a new session. The user has no equivalent. "User sends a message" and "user spawns a parallel task" are the same input channel, so one necessarily interrupts the other.

Proposed solution

Add a separate affordance in the GUI (e.g. a button, keyboard shortcut, or side-panel action) that lets the user spawn a new session without interrupting the active turn. Ideally:

• The new session inherits relevant context from the current conversation (repo, branch, recent file paths, etc.)
• The current turn continues uninterrupted
• The user can provide a short prompt for the new session (like "fix the stale import in utils/foo.ts")

This is the user-side equivalent of the assistant's spawn_task chip — a parallel task channel that doesn't compete with the primary conversation.

Why this matters

Power users working in long sessions frequently notice tangential issues mid-flow. Today they either lose those observations or break their momentum to capture them. A dedicated spawn affordance would let them capture work without context-switching.