Implements unified model routing

Migrates the AMP module to a new unified routing system, replacing the fallback handler with a router-based approach.

This change introduces a `ModelRoutingWrapper` that handles model extraction, routing decisions, and proxying based on provider availability and model mappings.
It provides a more flexible and maintainable routing mechanism by centralizing routing logic.

The changes include:
- Introducing new `routing` package with core routing logic.
- Creating characterization tests to capture existing behavior.
- Implementing model extraction and rewriting.
- Updating AMP module routes to utilize the new routing wrapper.
- Deprecating `FallbackHandler` in favor of the new `ModelRoutingWrapper`.

internal/routing/extractor.go

@@ -0,0 +1,59 @@
+package routing
+
+import (
+	"strings"
+
+	"github.com/tidwall/gjson"
+)
+
+// ModelExtractor extracts model names from request data.
+type ModelExtractor interface {
+	// Extract returns the model name from the request body and gin parameters.
+	// The ginParams map contains route parameters like "action" and "path".
+	Extract(body []byte, ginParams map[string]string) (string, error)
+}
+
+// DefaultModelExtractor is the standard implementation of ModelExtractor.
+type DefaultModelExtractor struct{}
+
+// NewModelExtractor creates a new DefaultModelExtractor.
+func NewModelExtractor() *DefaultModelExtractor {
+	return &DefaultModelExtractor{}
+}
+
+// Extract extracts the model name from the request.
+// It checks in order:
+// 1. JSON body "model" field (OpenAI, Claude format)
+// 2. "action" parameter for Gemini standard format (e.g., "gemini-pro:generateContent")
+// 3. "path" parameter for AMP CLI Gemini format (e.g., "/publishers/google/models/gemini-3-pro:streamGenerateContent")
+func (e *DefaultModelExtractor) Extract(body []byte, ginParams map[string]string) (string, error) {
+	// First try to parse from JSON body (OpenAI, Claude, etc.)
+	if result := gjson.GetBytes(body, "model"); result.Exists() && result.Type == gjson.String {
+		return result.String(), nil
+	}
+
+	// For Gemini requests, model is in the URL path
+	// Standard format: /models/{model}:generateContent -> :action parameter
+	if action, ok := ginParams["action"]; ok && action != "" {
+		// Split by colon to get model name (e.g., "gemini-pro:generateContent" -> "gemini-pro")
+		parts := strings.Split(action, ":")
+		if len(parts) > 0 && parts[0] != "" {
+			return parts[0], nil
+		}
+	}
+
+	// AMP CLI format: /publishers/google/models/{model}:method -> *path parameter
+	// Example: /publishers/google/models/gemini-3-pro-preview:streamGenerateContent
+	if path, ok := ginParams["path"]; ok && path != "" {
+		// Look for /models/{model}:method pattern
+		if idx := strings.Index(path, "/models/"); idx >= 0 {
+			modelPart := path[idx+8:] // Skip "/models/"
+			// Split by colon to get model name
+			if colonIdx := strings.Index(modelPart, ":"); colonIdx > 0 {
+				return modelPart[:colonIdx], nil
+			}
+		}
+	}
+
+	return "", nil
+}