Allow users to create subagents directly from the Subagents panel

Feature request

Add a + button to the Subagents section so users can create a subagent directly from the interface, without first asking the main session to create one.

Problem

When the main session already has a large prompt or a long-running task, asking it to create a subagent adds more instructions and coordination overhead to the main context. This can consume useful context and delay the primary task, even when the user simply wants to delegate an independent piece of work.

The current workflow makes the main session the mandatory entry point for subagent creation. That is inconvenient for parallel work, especially when the user already knows which task should be delegated.

Proposed workflow

1. The user clicks + beside Subagents.
2. Codex opens a new side chat dedicated to the subagent.
3. The user provides the subagent prompt in that side chat, without adding the full prompt to the main session.
4. The main session receives a lightweight notification that the side chat exists, without importing the entire subagent conversation into its context.
5. The subagent works independently and reports its status in the Subagents section.
6. When the subagent finishes, its result becomes available to the main session.
7. The main session can then take ownership of the result, review it, or continue the work based on the returned output.

Why this would help

This would make subagents useful for genuine parallel collaboration instead of requiring the main session to coordinate every delegation step. It would reduce unnecessary context growth, keep the primary task focused, and let users start independent work immediately from the visible Subagents panel.

The side chat should remain linked to the main session for status and final handoff, while keeping the full subagent prompt and intermediate work isolated unless the user or main session explicitly requests it.

Relationship to existing request

This complements #26227, which focuses on persisting side chats as child threads attached to the main thread. This request focuses on the user-facing creation flow: allowing a new subagent side chat to be started directly from the + button in the Subagents section.

UI reference

The intended location is the currently unused space on the right side of the Subagents row, matching the existing + buttons in the Outputs and Sources sections.