[BUG] VS Code extension: no colored status dots on session tabs (Remote-SSH, multiple sessions)

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) and this hasn't been reported yet
- [x] This is a single bug report (please file separate reports for different bugs)
- [x] I am using the latest version of Claude Code

### What's Wrong?

What's Wrong?

The colored status indicator dots on Claude Code session tabs (blue = permission pending, orange = unread completion) do not appear at all, on any version I have tried.

I run several Claude Code sessions in parallel, each as its own editor tab. No tab ever shows a dot, whether it is active or hidden, whether a session is waiting for permission approval or has finished its turn in the background.

Because of this I have no way to tell which session needs attention without clicking through every tab.

Environment
Claude Code VS Code extension: 2.1.272 (also tested 2.1.270 and the version prior to 2.1.272)
VS Code running on Windows, connected via Remote-SSH to a Linux host
Extension installed and enabled on the remote host ("Extension is enabled on 'SSH: i9'")
Native panel UI (not integrated terminal)
Several sessions open simultaneously as editor tabs
Steps to Reproduce
Connect VS Code to a remote Linux host via Remote-SSH
Open several Claude Code sessions, each as a separate editor tab
Let one session run until it requests permission, and another until it finishes its turn
Switch to a different tab so the sessions in question are hidden
Observe the tab icons
Expected Behavior

Hidden session tabs should show the colored indicator introduced in v2.0.73 — blue for a pending permission request, orange for an unread completion.

Actual Behavior

No dot appears on any tab, in any state.

What I Already Tried
Downgraded the extension to 2.1.270 and to the version before 2.1.272, via Install from VSIX (Linux 64-bit build, installed on the remote host) — no change
Reloaded the window after each install
Confirmed the extension is otherwise fully functional
Disabled Auto Update so the downgrades persisted

I could not test a purely local VS Code instance, as Claude Code does not load locally on this machine.

Is this a regression?

Yes. The dots were present and working before; they stopped appearing and have not returned on any version I tested.

Related

This may be the same underlying problem as the Remote-SSH case described in #78595, and possibly related to #37177.

### What Should Happen?

Hidden Claude Code session tabs should show the colored status indicator introduced in v2.0.73 — blue for a pending permission request, orange for an unread completion.

### Error Messages/Logs

```shell

```

### Steps to Reproduce

Connect VS Code on Windows to a remote Linux host via Remote-SSH
Open several Claude Code sessions, each as a separate editor tab
Let one session run until it requests permission, and another until it finishes its turn
Switch to a different tab so those sessions are hidden
Look at the tab icons — no colored dot appears in any state

### Claude Model

Not sure / Multiple models

### Is this a regression?

Yes, this worked in a previous version

### Last Working Version

_No response_

### Claude Code Version

2.1.271, i guess

### Platform

Anthropic API

### Operating System

Windows

### Terminal/Shell

VS Code integrated terminal

### Additional Information

_No response_

Start by reproducing the missing indicators in the VS Code extension with Windows Remote-SSH, multiple editor tabs, and the native panel UI. Compare permission-pending and unread-completion states across the reported versions, then review related issues #78595 and #37177. Done means hidden session tabs show blue or orange status dots in the affected setup.

Written by the indexing model from the issue text.