feat(amp): require API key authentication for management routes

All Amp management endpoints (e.g., /api/user, /threads) are now protected by the standard API key authentication middleware. This ensures that all management operations require a valid API key, significantly improving security.

As a result of this change:
- The `restrict-management-to-localhost` setting now defaults to `false`. API key authentication provides a stronger and more flexible security control than IP-based restrictions, improving usability in containerized environments.
- The reverse proxy logic now strips the client's `Authorization` header after authenticating the initial request. It then injects the configured `upstream-api-key` for the request to the upstream Amp service.

BREAKING CHANGE: Amp management endpoints now require a valid API key for authentication. Requests without a valid API key in the `Authorization` header will be rejected with a 401 Unauthorized error.

internal/api/modules/amp/proxy.go

@@ -41,6 +41,11 @@ func createReverseProxy(upstreamURL string, secretSource SecretSource) (*httputi
 		originalDirector(req)
 		req.Host = parsed.Host
 
+		// Remove client's Authorization header - it was only used for CLI Proxy API authentication
+		// We will set our own Authorization using the configured upstream-api-key
+		req.Header.Del("Authorization")
+		req.Header.Del("X-Api-Key")
+
 		// Preserve correlation headers for debugging
 		if req.Header.Get("X-Request-ID") == "" {
 			// Could generate one here if needed
@@ -50,7 +55,7 @@ func createReverseProxy(upstreamURL string, secretSource SecretSource) (*httputi
 		// Users going through ampcode.com proxy are paying for the service and should get all features
 		// including 1M context window (context-1m-2025-08-07)
 
-		// Inject API key from secret source (precedence: config > env > file)
+		// Inject API key from secret source (only uses upstream-api-key from config)
 		if key, err := secretSource.Get(req.Context()); err == nil && key != "" {
 			req.Header.Set("X-Api-Key", key)
 			req.Header.Set("Authorization", fmt.Sprintf("Bearer %s", key))