Fix router state after client side navigation (#4383)

* Fix router state after client side navigation

* add client side navigation to the fullstack routing spec

* fix playwright test

packages/fullstack-protocol/src/lib.rs

@@ -144,6 +144,19 @@ impl<T> SerializeContextEntry<T> {
     }
 }
 
+/// Check if the client is currently rendering a component for hydration. Always returns true on the server.
+pub fn is_hydrating() -> bool {
+    #[cfg(feature = "web")]
+    {
+        // On the client, we can check if the context is set
+        CONTEXT.with(|context| context.borrow().is_some())
+    }
+    #[cfg(not(feature = "web"))]
+    {
+        true
+    }
+}
+
 /// Get or insert the current serialize context. On the client, the hydration context this returns
 /// will always return `TakeDataError::DataNotAvailable` if hydration of the current chunk is finished.
 pub fn serialize_context() -> HydrationContext {