Add socket-level websocket connection health checking

Implements proper socket-level health checking for gateway websocket connections:

- Add is_connection_alive() method to GatewayTransceiver trait
- Implement socket-level health check using TcpStream::peek() on Unix systems
- Add is_gateway_connection_alive() method to MixnetClient for easy access
- Update network monitor to use connection health checks before sending
- Fix axum router state configuration in network monitor

The health check performs actual OS-level socket validation rather than just
checking file descriptor existence, providing reliable connection status.

common/client-core/src/client/mix_traffic/transceiver.rs

@@ -36,6 +36,9 @@ pub trait GatewayTransceiver: GatewaySender + GatewayReceiver {
         &mut self,
         message: ClientRequest,
     ) -> Result<(), GatewayClientError>;
+    
+    /// Check if the websocket connection to the gateway is alive
+    fn is_connection_alive(&self) -> bool;
 }
 
 /// This trait defines the functionality of sending `MixPacket` into the mixnet,
@@ -90,6 +93,11 @@ impl<G: GatewayTransceiver + ?Sized + Send> GatewayTransceiver for Box<G> {
         log::debug!("Sent client request: {:?}", message);
         Ok(())
     }
+    
+    #[inline]
+    fn is_connection_alive(&self) -> bool {
+        (**self).is_connection_alive()
+    }
 }
 
 #[cfg_attr(target_arch = "wasm32", async_trait(?Send))]
@@ -147,6 +155,10 @@ where
     ) -> Result<(), GatewayClientError> {
         self.gateway_client.send_client_request(message).await
     }
+    
+    fn is_connection_alive(&self) -> bool {
+        self.gateway_client.is_connection_alive()
+    }
 }
 
 #[cfg_attr(target_arch = "wasm32", async_trait(?Send))]
@@ -234,6 +246,11 @@ mod nonwasm_sealed {
         ) -> Result<(), GatewayClientError> {
             Ok(())
         }
+        
+        fn is_connection_alive(&self) -> bool {
+            // LocalGateway is always "connected" since it's in-process
+            true
+        }
     }
 
     #[async_trait]
@@ -316,4 +333,9 @@ impl GatewayTransceiver for MockGateway {
     ) -> Result<(), GatewayClientError> {
         Ok(())
     }
+    
+    fn is_connection_alive(&self) -> bool {
+        // MockGateway is always "connected" for testing purposes
+        true
+    }
 }