Background subagent is not visible in the chat that spawned it

## Type of issue

Bug

## Description

When a chat starts a subagent through the background `task` mechanism, the subagent appears as a running item in the Sessions sidebar, but the chat that spawned it shows no persistent indication that a subagent is running. There is no visible status or link in the parent transcript that lets the user understand or navigate to the delegated work.

This is especially confusing when the parent chat is idle or appears complete while its delegated work is still running elsewhere.

## Expected behavior

The spawning chat should show a persistent, accessible representation of the background subagent, including its current status and a way to open it.

## Actual behavior

The background subagent is visible in the Sessions sidebar only. The parent chat does not expose it outside of the generic/collapsed task execution history.

## Notes

The existing Subagents pill derives its entries from tool-origin chats in the same session (`ChatOriginKind.Tool` with a matching `parentChat`). A background `task` subagent is represented as a separate agent session instead, so it does not enter that collection. The richer session-result link is also currently associated with completed `create_session`/`create_chat` tool calls carrying `sessionCreated` data, rather than the live background-task lifecycle.

@justschen I can share screenshots demonstrating the behavior with you in Slack; I have intentionally not attached them here.