Refactor API handlers organization and simplify error response handling

- Modularized handlers into dedicated packages (`gemini`, `claude`, `cli`) for better structure.
- Centralized `ErrorResponse` and `ErrorDetail` types under `handlers` package for reuse.
- Updated all handlers to utilize the shared `ErrorResponse` model.
- Introduced specialization of handler structs (`GeminiAPIHandlers`, `ClaudeCodeAPIHandlers`, `GeminiCLIAPIHandlers`) for improved clarity and separation of concerns.
- Refactored `getClient` logic with additional properties and better state management.

Refactor `translator` package by modularizing code for `claude` and `gemini`

- Moved Claude-specific logic (`PrepareClaudeRequest`, `ConvertCliToClaude`) to `translator/claude/code`.
- Moved Gemini-specific logic (`FixCLIToolResponse`) to `translator/gemini/cli` for better package structure.
- Updated affected handler imports and method references.

Add comprehensive package-level documentation across key modules

- Introduced detailed package-level documentation for core modules: `auth`, `client`, `cmd`, `handlers`, `util`, `watcher`, `config`, `translator`, and `api`.
- Enhanced code readability and maintainability by clarifying the purpose and functionality of each package.
- Aligned documentation style and tone with existing codebase conventions.

Refactor API handlers and translator modules for improved clarity and consistency

- Standardized handler struct names (`GeminiAPIHandlers`, `ClaudeCodeAPIHandlers`, `GeminiCLIAPIHandlers`, `OpenAIAPIHandlers`) and updated related comments.
- Fixed unnecessary `else` blocks in streaming logic for cleaner error handling.
- Renamed variables for better readability (`responseIdResult` to `responseIDResult`, `activationUrl` to `activationURL`, etc.).
- Addressed minor inconsistencies in API handler comments and SSE header initialization.
- Improved modularization of `claude` and `gemini` translator components.

Standardize configuration field naming for consistency across modules

- Renamed `ProxyUrl` to `ProxyURL`, `ApiKeys` to `APIKeys`, and `ConfigQuotaExceeded` to `QuotaExceeded`.
- Updated all relevant references and comments in `config`, `auth`, `api`, `util`, and `watcher`.
- Ensured consistent casing for `GlAPIKey` debug logs.

internal/auth/auth.go

@@ -1,3 +1,6 @@
+// Package auth provides OAuth2 authentication functionality for Google Cloud APIs.
+// It handles the complete OAuth2 flow including token storage, web-based authentication,
+// proxy support, and automatic token refresh. The package supports both SOCKS5 and HTTP/HTTPS proxies.
 package auth
 
 import (
@@ -39,7 +42,7 @@ var (
 // initiating a new web-based OAuth flow if necessary, and refreshing tokens.
 func GetAuthenticatedClient(ctx context.Context, ts *TokenStorage, cfg *config.Config) (*http.Client, error) {
 	// Configure proxy settings for the HTTP client if a proxy URL is provided.
-	proxyURL, err := url.Parse(cfg.ProxyUrl)
+	proxyURL, err := url.Parse(cfg.ProxyURL)
 	if err == nil {
 		var transport *http.Transport
 		if proxyURL.Scheme == "socks5" {