Migrate App Proxy to use common UnifiedConfig infrastructure

[HyeockJinKim]

Motivation

Refactor App Proxy's config to use the consolidated common config classes, reducing code duplication.

Required Features

Files to modify:

• src/ai/backend/appproxy/coordinator/config.py
• src/ai/backend/appproxy/worker/config.py (if exists)
• Related imports in App Proxy codebase

Changes:

• Import common config classes from ai.backend.common.configs.unified
• Keep App Proxy-specific configs (AppProxyConfig, CoordinatorConfig, etc.) in place
• Update config classes to compose common configs
• Ensure backward compatibility with existing config loading

Impact

• App Proxy coordinator and worker components
• Config loading from TOML and etcd

Testing Scenarios

• App Proxy uses common config classes
• All existing functionality preserved
• Tests pass
• Config loading from TOML/etcd works correctly

JIRA Issue: BA-3773