Show status indicators on chat tabs: in-progress spinner, ready to review, and waiting for user

## Problem

When multiple chat tabs are open in a workspace (or when switching between code/spec tabs and chats), all chat tabs look identical regardless of their current agent status.

While #273 added per-workspace status in the Projects rail, users running concurrent chats or multiple tasks within a workspace still need to manually switch tabs to check execution progress.

## Proposed solution

Add visual state indicators directly on chat tabs in the tab strip:

1. **In-progress / working**: An active spinner or animated working glyph while the agent session is streaming, executing tools, or draining queued turns.
2. **Needs user / asks something**: An attention indicator (e.g. question mark badge or distinct highlight) when the session is waiting on `ask_user_question` or pending UI input, so the user knows action is needed.
3. **Ready to review / settled**: A clear completion marker (e.g. checkmark or subtle status pill) indicating that an agent turn has settled and changes/output are ready to be reviewed.
4. **Error**: An indicator when a turn halts on an error or failure stop reason.

## Alternatives considered

- Relying solely on the Projects rail status (#273): Does not differentiate between multiple chat tabs within the same workspace.

## Additional context

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🤖 Generated by AI agent

The issue names no files or tests; start by locating the chat tab strip and the agent session status events used by the existing Projects rail status. Done means tabs visibly distinguish working, waiting for user, settled and error states while multiple chats can remain open.

Written by the indexing model from the issue text.