UI: "API Usage Billing" label shown even when using local LLM - misleading

Describe the bug

When using Claude Code with a local LLM (not the Anthropic API), the UI footer still displays "API Usage Billing" text. This is misleading as it suggests billing is occurring even when no API calls are being made to Anthropic.

Steps to reproduce

1. Configure Claude Code to use a local LLM (e.g., via Ollama)
2. Run claude or claude --dangerously-skip-permissions
3. Observe the footer text showing "API Usage Billing"

Expected behavior

The UI should either:

• Hide the "API Usage Billing" text when using a local LLM
• Show "Local Model" or similar text to indicate no API billing is occurring
• Only display "API Usage Billing" when actually connected to Anthropic's API

Screenshots

<img width="622" height="60" alt="Image" src="https://github.com/user-attachments/assets/b27d2362-3929-4e7f-bd57-8736f3b5deed" />

Environment

• OS: macOS (Darwin 25.3.0)
• Claude Code version: v2.1.81
• Local LLM: qwen-3.5-397b

Additional context

While this is a cosmetic issue and no actual billing occurs, it creates confusion for users who have set up local LLMs to avoid API costs. The label should accurately reflect the current connection type.