[FEATURE] Add status indicator on the side bar history conversations

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

When working with multiple conversations in parallel (8–10 in my case), there's no way to tell at a glance which conversations are still being processed by Claude and which are idle/done. I have to open each one individually to check its state, which is tedious.

The Session History panel in the VSCode extension lists conversations by title but shows no activity status.

Proposed Solution

Add a small status indicator (e.g. a colored dot) next to each conversation in the Sessions panel:

Active/busy — Claude is currently processing
Waiting for input — Claude is paused on a permission/input request
Idle — nothing running

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

This is especially valuable since the extension is built for parallel/multi-agent workflows. Right now the UX doesn't support quickly scanning which sessions need attention.

Additional Context

_No response_