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

examples/custom-provider/main.go

@@ -137,6 +137,10 @@ func (MyExecutor) Execute(ctx context.Context, a *coreauth.Auth, req clipexec.Re
 	return clipexec.Response{Payload: body}, nil
 }
 
+func (MyExecutor) CountTokens(context.Context, *coreauth.Auth, clipexec.Request, clipexec.Options) (clipexec.Response, error) {
+	return clipexec.Response{}, errors.New("count tokens not implemented")
+}
+
 func (MyExecutor) ExecuteStream(ctx context.Context, a *coreauth.Auth, req clipexec.Request, opts clipexec.Options) (<-chan clipexec.StreamChunk, error) {
 	ch := make(chan clipexec.StreamChunk, 1)
 	go func() {