[Feature Request] Add statusLine support to VS Code native extension

Bug Description
Feature request: statusLine support in the VS Code native extension

The Claude Code CLI has a great statusLine.command config hook that lets you
render persistent context %, token usage, 5h/7d quota, model badge, git status,
and tools activity in a bar beneath the input field. The community plugin
claude-hud (jarrodwatts/claude-hud) does exactly this and is invaluable for
power users on long, context-heavy sessions — you can see at a glance when to
/save before auto-compact kicks in, how much of your weekly Opus quota you've
burned, and what the model is currently doing.

The VS Code native extension currently has none of this. The only context
visibility is the one-shot /usage command and a small footer indicator in the
prompt box. There's no persistent HUD, no equivalent statusLine hook, and no
documented extension API for a third-party VS Code extension to subscribe to
session state and build one.

Use case: I'm a heavy user of the VS Code native extension because I like the
UI, file integration, and the side-by-side editing. But I find myself dropping
back to the CLI in the integrated terminal whenever I need claude-hud's
visibility for a multi-hour, multi-PR session — which fragments my workflow.

Two paths that would solve this:

1. Add statusLine.command support to the VS Code extension so existing CLI

plugins like claude-hud Just Work. The output could render in a sidebar
panel, a status bar item, a webview footer, or a small persistent strip
beneath the chat panel.

1. Expose a documented extension API (or hooks/events) so third-party VS Code

extensions can subscribe to session state — context window %, token counts,
rate limit usage, model, current tool activity, project/git state — and
build their own status displays.

Either would be a huge productivity win for users who want the visibility of
claude-hud without leaving the VS Code extension UI.

Environment Info

• Platform: linux
• Terminal: vscode
• Version: 2.1.92
• Feedback ID: ad199ad0-ba6f-46f4-8fd2-d500de73f9fa