feat: Add Amp CLI integration with comprehensive documentation

Add full Amp CLI support to enable routing AI model requests through the proxy
while maintaining Amp-specific features like thread management, user info, and
telemetry. Includes complete documentation and pull bot configuration.

Features:
- Modular architecture with RouteModule interface for clean integration
- Reverse proxy for Amp management routes (thread/user/meta/ads/telemetry)
- Provider-specific route aliases (/api/provider/{provider}/*)
- Secret management with precedence: config > env > file
- 5-minute secret caching to reduce file I/O
- Automatic gzip decompression for responses
- Proper connection cleanup to prevent leaks
- Localhost-only restriction for management routes (configurable)
- CORS protection for management endpoints

Documentation:
- Complete setup guide (USING_WITH_FACTORY_AND_AMP.md)
- OAuth setup for OpenAI (ChatGPT Plus/Pro) and Anthropic (Claude Pro/Max)
- Factory CLI config examples with all model variants
- Amp CLI/IDE configuration examples
- tmux setup for remote server deployment
- Screenshots and diagrams

Configuration:
- Pull bot disabled for this repo (manual rebase workflow)
- Config fields: AmpUpstreamURL, AmpUpstreamAPIKey, AmpRestrictManagementToLocalhost
- Compatible with upstream DisableCooling and other features

Technical details:
- internal/api/modules/amp/: Complete Amp routing module
- sdk/api/httpx/: HTTP utilities for gzip/transport
- 94.6% test coverage with 34 comprehensive test cases
- Clean integration minimizes merge conflict risk

Security:
- Management routes restricted to localhost by default
- Configurable via amp-restrict-management-to-localhost
- Prevents drive-by browser attacks on user data

This provides a production-ready foundation for Amp CLI integration while
maintaining clean separation from upstream code for easy rebasing.

Amp-Thread-ID: https://ampcode.com/threads/T-9e2befc5-f969-41c6-890c-5b779d58cf18

internal/api/server.go

@@ -21,6 +21,8 @@ import (
 	"github.com/router-for-me/CLIProxyAPI/v6/internal/access"
 	managementHandlers "github.com/router-for-me/CLIProxyAPI/v6/internal/api/handlers/management"
 	"github.com/router-for-me/CLIProxyAPI/v6/internal/api/middleware"
+	"github.com/router-for-me/CLIProxyAPI/v6/internal/api/modules"
+	ampmodule "github.com/router-for-me/CLIProxyAPI/v6/internal/api/modules/amp"
 	"github.com/router-for-me/CLIProxyAPI/v6/internal/config"
 	"github.com/router-for-me/CLIProxyAPI/v6/internal/logging"
 	"github.com/router-for-me/CLIProxyAPI/v6/internal/managementasset"
@@ -261,6 +263,20 @@ func NewServer(cfg *config.Config, authManager *auth.Manager, accessManager *sdk
 
 	// Setup routes
 	s.setupRoutes()
+
+	// Register Amp module using V2 interface with Context
+	ampModule := ampmodule.NewLegacy(accessManager, AuthMiddleware(accessManager))
+	ctx := modules.Context{
+		Engine:         engine,
+		BaseHandler:    s.handlers,
+		Config:         cfg,
+		AuthMiddleware: AuthMiddleware(accessManager),
+	}
+	if err := modules.RegisterModule(ctx, ampModule); err != nil {
+		log.Errorf("Failed to register Amp module: %v", err)
+	}
+
+	// Apply additional router configurators from options
 	if optionState.routerConfigurator != nil {
 		optionState.routerConfigurator(engine, s.handlers, cfg)
 	}