[FEATURE] Display Backend Connection Type in UI

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Summary

Add a visual indicator showing which backend (AWS Bedrock vs Anthropic Direct) is being used for model inference.

Currently, the "Account & Usage..." menu shows Anthropic account information even when using AWS Bedrock as the inference backend. This creates confusion because:

1. Users authenticate with Anthropic (for Claude Code license)
2. But inference may route through AWS Bedrock (via CLAUDE_CODE_USE_BEDROCK=1)
3. The UI doesn't distinguish between these two separate concerns

This makes it difficult to verify at a glance which backend is actively handling requests.

Current Behavior

• User sets CLAUDE_CODE_USE_BEDROCK=1 in ~/.claude/settings.json
• All model inference goes through AWS Bedrock (confirmed by model ID format: eu.anthropic.claude-sonnet-4-5-20250929-v1:0)
• "Account & Usage..." still shows Anthropic account info
• No visual indicator confirms Bedrock is being used

Proposed Solution

Add backend connection indicator in one or more locations:

Option 1: Status Bar Item (Preferred)

Display backend type in VSCode status bar:

• When using Bedrock: 🔶 Bedrock (eu-west-1)
• When using Direct API: 🟣 Anthropic API
• Make it clickable to show details (region, profile, model ID)

Option 2: Account & Usage Menu

Add a "Connection" section showing:

Connection Type: AWS Bedrock
Region: eu-west-1
Profile: dnd-non-prod
Model: eu.anthropic.claude-sonnet-4-5-20250929-v1:0

Option 3: Chat Panel Header

Display small badge next to model selector showing backend type

Benefits

1. Clarity: Users immediately know which backend is handling requests
2. Debugging: Easier to troubleshoot authentication/connection issues
3. Compliance: Important for teams with specific backend requirements
4. Cost Tracking: Users can verify they're using the intended billing source

Alternative Solutions

Users can:

• Check model ID format in conversation (but requires starting a chat)
• Add SessionStart hooks to display connection info (not visible in UI)
• Add statusLine config (CLI only, not in VSCode extension)
• Check CLAUDE_CODE_USE_BEDROCK env var manually

These workarounds are not discoverable or user-friendly.

Priority

Low - Nice to have

Feature Category

Configuration and settings

Use Case Example

_No response_

Additional Context

• Environment: VSCode Extension
• Configuration: ~/.claude/settings.json
• Related settings: CLAUDE_CODE_USE_BEDROCK, AWS_REGION, AWS_PROFILE, awsAuthRefresh