VS Code extension shows 'Claude API' instead of subscription plan in status line

Description

The VS Code extension displays "Claude API" in the status line instead of showing the actual subscription plan (e.g., "Claude Max"), while the standalone CLI correctly displays the full subscription information.

Steps to Reproduce

1. Have a Claude Max subscription
2. Login via /login in both VS Code extension and standalone CLI
3. Compare the status line display

Expected Behavior

VS Code extension should show subscription details similar to CLI:

Opus 4.5 · Claude Max · user@email.com's Organization

Actual Behavior

VS Code extension shows:

Opus 4.5 · Claude API

CLI correctly shows:

Opus 4.5 · Claude Max · marvinfs@gmail.com's Organization

Screenshots

VS Code extension (incorrect):

<img width="785" height="306" alt="Image" src="https://github.com/user-attachments/assets/8bd7ab18-396d-461d-93e8-6fbd805a1ce7" />

CLI (correct):

<img width="1107" height="450" alt="Image" src="https://github.com/user-attachments/assets/7b669d17-3899-43c9-8377-e312a7acf434" />

Environment

• OS: Windows 11 25H2
• VS Code Extension Version: 2.0.75
• CLI Version: 2.0.76
• Subscription: Claude Max

Additional Context

• The credentials file (~/.claude/.credentials.json) correctly contains subscriptionType: "max" and rateLimitTier: "default_claude_max_5x"
• Re-logging in via /login in VS Code does not fix the issue
• The actual functionality works correctly (MAX rate limits are applied), this is purely a display issue
• Both CLI and VS Code extension read from the same credentials file

This appears to be a cosmetic bug in how the VS Code extension renders the status line compared to the standalone CLI.