VSCode: Add loading/spinner indicator to tabs while Claude is processing

Feature Request

Problem:
When using Claude Code in the VSCode extension with multiple tabs, there's no visual indicator on a tab to show that Claude is actively processing/running. The current dot indicators only show:

• Blue: permission request pending
• Orange: finished while tab was hidden

There's no indicator for the "currently running" state, making it hard to know at a glance which tabs are still working.

Proposed Solution:
Add a visible loading indicator (spinner, animated icon, or pulsing dot) on the tab icon while Claude is actively generating a response. This would make it easy to see which tabs are still processing without needing to switch to them.

Use Case:
When working with multiple Claude tabs simultaneously, users need to quickly identify which conversations are still running vs. idle. This is especially important for users who only use Claude Code within VSCode (not the terminal), where the status line workaround isn't available.

Alternatives Considered:

• Status line in terminal — not applicable for VSCode-only users
• Keeping the panel visible — doesn't scale with multiple tabs
• Custom CSS extensions — can't detect Claude's internal state

🤖 Generated with Claude Code