Rewrite Client SDK based on Pydantic API Models

## Overview

Rewrite Backend.AI Client SDK to leverage the Pydantic-based API models, providing type-safe client interfaces with auto-completion and validation.

## Goals

- Generate client code from Pydantic API models
- Provide type-safe API client interfaces
- Enable IDE auto-completion for all API methods
- Add client-side validation using Pydantic models
- Maintain backward compatibility where possible

## Scope

Rewrite all client SDK modules corresponding to API domains:

- Authentication & Authorization Client
- Session Management Client
- Virtual Folder Client
- User & Group Management Client
- Resource Management Client
- Container Registry Client
- Scaling Group Client
- Template Management Client
- Admin Operations Client
- Monitoring & Logs Client

## Success Criteria

- All client methods have type-safe interfaces
- Full IDE auto-completion support
- Client-side validation using Pydantic models
- All existing client tests pass
- Type checking passes with no regressions

## Dependencies

- Blocked by: Manager API Pydantic Migration Epic (BA-2628)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

JIRA Issue: BA-2629