[VS Code] /rename doesn't repaint sidebar/tab until Developer: Reload Window + a click

### Summary

In the Claude Code **VS Code native extension**, renaming a session via `/rename` succeeds at the data layer but the **Session history sidebar entry and the tab title do not repaint** until a `Developer: Reload Window` **and** a subsequent manual click. This makes it very hard to tell concurrent Claude windows apart, which defeats the purpose of naming them.

This is the same substance as **#63465** ("Chat session rename doesn't update in sidebar until VS Code restarts"), which was closed as *not planned* / inactive rather than fixed — its closing comment invited a fresh issue if still relevant. It still is. Also related: **#53942**, **#37628**.

### Steps to reproduce

1. In an active session, run `/rename `. The command output confirms `Session renamed to: ` — the rename is applied at the data layer.
2. Observe the Session history sidebar entry and the tab title.

### Expected

The sidebar entry and tab title update to `` immediately on rename.

### Actual

They keep showing the old auto-generated title. Specifically:

- Clicking to another session and back does **not** refresh the label.
- Collapsing/expanding the Session history panel does **not** refresh it.
- Only `Developer: Reload Window` refreshes it — and **even then** the label does not update until a session is clicked afterward.

The session-history list appears not to subscribe to rename events, and the post-reload render needs a focus/selection change to repaint.

### Impact

Users running multiple concurrent Claude windows can't distinguish them by name until they reload the window and click around, which defeats the purpose of naming sessions. Current workaround is the full `/rename` → Reload Window → click-a-session dance.

### Environment

- Claude Code **VS Code native extension** (sidebar Session history + tabs)
- macOS (darwin)

Start at the VS Code native extension's `/rename` command and follow how the Session history sidebar entry and tab title receive session updates. Check whether rename events reach both renderers and reproduce the reload-and-click behavior; done means both labels update immediately after renaming, without reloading or changing selection.

Written by the indexing model from the issue text.