feat(services): add OpenClaw branches to backend services

- Add OpenClaw branches to proxy service (not supported)
- Add OpenClaw to MCP service (skip sync, MCP still in development)
- Add OpenClaw skills directory path
- Update ProxyTakeoverStatus with openclaw field
- Add OpenClaw to stream check (not supported)

src-tauri/src/proxy/providers/mod.rs

@@ -136,6 +136,10 @@ impl ProviderType {
                 // OpenCode doesn't support proxy, but return a default type for completeness
                 ProviderType::Codex // Fallback to Codex-like type
             }
+            AppType::OpenClaw => {
+                // OpenClaw doesn't support proxy, but return a default type for completeness
+                ProviderType::Codex // Fallback to Codex-like type
+            }
         }
     }
 
@@ -184,6 +188,10 @@ pub fn get_adapter(app_type: &AppType) -> Box<dyn ProviderAdapter> {
             // OpenCode doesn't support proxy, fallback to Codex adapter
             Box::new(CodexAdapter::new())
         }
+        AppType::OpenClaw => {
+            // OpenClaw doesn't support proxy, fallback to Codex adapter
+            Box::new(CodexAdapter::new())
+        }
     }
 }