fix(amp): enable OAuth fallback for Gemini v1beta1 routes

AMP CLI sends Gemini requests to non-standard paths that were being
directly proxied to ampcode.com without checking for local OAuth.

This fix adds:
- GeminiBridge handler to transform AMP CLI paths to standard format
- Enhanced model extraction from AMP's /publishers/google/models/* paths
- FallbackHandler wrapper to check for local OAuth before proxying

Flow:
- If user has local Google OAuth → use it (free tier)
- If no local OAuth → fallback to ampcode.com (charges credits)

Fixes issue where gemini-3-pro-preview requests always charged AMP
credits even when user had valid Google Cloud OAuth configured.

internal/api/modules/amp/fallback_handlers.go

@@ -102,8 +102,8 @@ func extractModelFromRequest(body []byte, c *gin.Context) string {
 		}
 	}
 
-	// For Gemini requests, model is in the URL path: /models/{model}:generateContent
-	// Extract from :action parameter (e.g., "gemini-pro:generateContent")
+	// For Gemini requests, model is in the URL path
+	// Standard format: /models/{model}:generateContent -> :action parameter
 	if action := c.Param("action"); action != "" {
 		// Split by colon to get model name (e.g., "gemini-pro:generateContent" -> "gemini-pro")
 		parts := strings.Split(action, ":")
@@ -112,5 +112,18 @@ func extractModelFromRequest(body []byte, c *gin.Context) string {
 		}
 	}
 
+	// AMP CLI format: /publishers/google/models/{model}:method -> *path parameter
+	// Example: /publishers/google/models/gemini-3-pro-preview:streamGenerateContent
+	if path := c.Param("path"); 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]
+			}
+		}
+	}
+
 	return ""
 }