[BUG] Account & Usage panel shows "Claude pro" instead of "Max plan" in VSCode extension (Windows)

Bug Description

The Account & Usage panel in the Claude Code VSCode/VSCodium extension displays \"Claude pro\" under the Plan field, despite the account being on the Max plan (confirmed via claude.ai/settings/billing).

Environment

• Claude Code extension: VSCodium (VSCode-compatible)
• OS: Windows 11 Home (10.0.26200)
• Auth method: Claude AI
• Plan (actual): Claude Max — auto-renews May 16, 2026
• Plan (shown in extension): Claude pro

Steps to Reproduce

1. Open Claude Code extension in VSCode / VSCodium
2. Click account icon → open Account & Usage panel
3. Observe the Plan field

Expected Behavior

Plan field should display "Max plan" (or equivalent) for Max plan subscribers.

Actual Behavior

Plan field displays "Claude pro" regardless of actual subscription tier.

Screenshots

Account & Usage panel (extension) — shows "Claude pro":

Plan: Claude pro

claude.ai/settings/billing (ground truth) — shows "Max plan":

Max plan · 5x more usage than Pro · auto-renews May 16, 2026

Additional Context

Related to #43851 (status line shows "Claude Pro" instead of "Claude Max" on macOS/CLI), but this affects a different UI surface: the Account & Usage panel inside the VSCode extension on Windows. The root cause may be shared — the extension likely reads a plan label that maps both Max and Pro to the same display string.